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Author ID: algaba.antonio Recent zbMATH articles by "Algaba, Antonio"
Published as: Algaba, Antonio; Algaba, A.
all top 5

Serials

15 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
11 Communications in Nonlinear Science and Numerical Simulation
10 Journal of Mathematical Analysis and Applications
10 Nonlinear Dynamics
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
6 Applied Mathematics and Computation
6 Qualitative Theory of Dynamical Systems
4 Physics Letters. A
4 Chaos, Solitons and Fractals
3 Journal of Computational and Applied Mathematics
3 Journal of Differential Equations
3 Physica D
3 Mediterranean Journal of Mathematics
2 Nonlinearity
2 Rocky Mountain Journal of Mathematics
2 Acta Applicandae Mathematicae
2 Applied Mathematics Letters
2 European Journal of Applied Mathematics
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Bulletin des Sciences Mathématiques
2 Discrete and Continuous Dynamical Systems
2 Chaos
2 Nonlinear Analysis. Real World Applications
2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis
2 Communications on Pure and Applied Analysis
1 Journal of Sound and Vibration
1 Physica A
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Mathematics and Computers in Simulation
1 Applied Mathematics and Mechanics. (English Edition)
1 Bulletin of the Belgian Mathematical Society - Simon Stevin
1 Differential Equations and Dynamical Systems
1 Abstract and Applied Analysis
1 Acta Mathematica Sinica. English Series
1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms
1 International Journal of Pure and Applied Mathematics
1 SIAM Journal on Applied Dynamical Systems
1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA

Publications by Year

Citations contained in zbMATH Open

112 Publications have been cited 1,022 times in 411 Documents Cited by Year
The integrability problem for a class of planar systems. Zbl 1165.34023
Algaba, A.; Gamero, E.; García, C.
58
2009
A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. Zbl 1043.37042
Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A.
34
2002
Hypernormal form for the Hopf-zero bifurcation. Zbl 0996.37062
Algaba, A.; Freire, E.; Gamero, E.
32
1998
Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system. Zbl 1323.37020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
32
2013
Isochronicity via normal form. Zbl 1021.34022
Algaba, Antonio; Freire, Emilio; Gamero, Estanislao
30
2000
Centers of quasi-homogeneous polynomial planar systems. Zbl 1238.34052
Algaba, A.; Fuentes, N.; García, C.
28
2012
Quasi-homogeneous normal forms. Zbl 1022.34034
Algaba, A.; Freire, E.; Gamero, E.; García, C.
28
2003
The center problem for a family of systems of differential equations having a nilpotent singular point. Zbl 1156.34031
Algaba, A.; García, C.; Reyes, M.
25
2008
Integrability of two dimensional quasi-homogeneous polynomial differential systems. Zbl 1213.37093
Algaba, A.; García, C.; Reyes, M.
24
2011
The Lü system is a particular case of the Lorenz system. Zbl 1301.37020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
24
2013
Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems. Zbl 1266.37023
Algaba, A.; García, C.; Reyes, M.
22
2012
Some results on Chua’s equation near a triple-zero linear degeneracy. Zbl 1083.93020
Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
21
2003
A tame degenerate Hopf-pitchfork bifurcation in a modified van der Pol-Duffing oscillator. Zbl 0976.70016
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
20
2000
On the Hopf-pitchfork bifurcation in the Chua’s equation. Zbl 1090.34545
Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
18
2000
Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator. Zbl 0928.70042
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
17
1998
Computing center conditions for vector fields with constant angular speed. Zbl 1032.34026
Algaba, A.; Reyes, M.
17
2003
A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation. Zbl 0943.34027
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
16
1999
Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems. Zbl 1192.34035
Algaba, A.; Freire, E.; Gamero, E.; García, C.
16
2010
Characterization of a monodromic singular point of a planar vector field. Zbl 1226.34031
Algaba, A.; García, C.; Reyes, M.
14
2011
Hypernormal form calculation for triple-zero degeneracies. Zbl 0988.37062
Gamero, E.; Freire, E.; Rodríguez-Luis, A. J.; Ponce, E.; Algaba, A.
13
1999
Hypernormal forms for equilibria of vector fields. Codimension one linear degeneracies. Zbl 0930.34027
Algaba, A.; Freire, E.; Gamero, E.
13
1999
An algorithm for computing quasi-homogeneous formal normal forms under equivalence. Zbl 1063.34029
Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; García, Cristóbal
13
2004
The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields. Zbl 1395.34047
Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume
13
2018
Reversibility and quasi-homogeneous normal forms of vector fields. Zbl 1202.34069
Algaba, A.; García, C.; Teixeira, M. A.
12
2010
On orbital-reversibility for a class of planar dynamical systems. Zbl 1337.34039
Algaba, A.; Checa, I.; García, C.; Gamero, E.
12
2015
Analytic integrability for some degenerate planar vector fields. Zbl 1306.34046
Algaba, Antonio; García, Cristóbal; Giné, Jaume
12
2014
Like-linearizations of vector fields. Zbl 1196.37080
Algaba, A.; García, C.; Reyes, M.
11
2009
Characterizing isochronous points and computing isochronous sections. Zbl 1208.34034
Algaba, A.; Reyes, M.
11
2009
On a codimension-three unfolding of the interaction of degenerate Hopf and pitchfork bifurcations. Zbl 0983.37057
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
11
1999
A bifurcation analysis of a simple electronic circuit. Zbl 1064.34030
Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J.
11
2005
Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations. Zbl 0999.37035
Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Merino, M.; Rodríguez-Luis, A. J.
11
2002
A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form. Zbl 1430.37054
Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
11
2019
Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations. Zbl 1201.34061
Algaba, A.; García, C.; Reyes, M.
10
2009
Nilpotent centres via inverse integrating factors. Zbl 1384.34037
Algaba, Antonio; García, Cristóbal; Giné, Jaume
10
2016
Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems. Zbl 1201.34050
Algaba, A.; García, C.; Reyes, M.
10
2010
Analytic integrability around a nilpotent singularity. Zbl 1432.34002
Algaba, Antonio; García, Cristóbal; Giné, Jaume
10
2019
Resonances of periodic orbits in Rössler system in presence of a triple-zero bifurcation. Zbl 1145.37322
Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; Rodríguez-Luis, Alejandro J.
9
2007
Takens-Bogdanov bifurcations of periodic orbits and Arnold’s tongues in a three-dimensional electronic model. Zbl 1090.37543
Algaba, A.; Merino, M.; Rodríguez-Luis, A. J.
9
2001
A class of non-integrable systems admitting an inverse integrating factor. Zbl 1333.37076
Algaba, A.; Fuentes, N.; García, C.; Reyes, M.
9
2014
The center problem. A view from the normal form theory. Zbl 1329.34071
Algaba, A.; Gamero, E.; García, C.
9
2016
Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Zbl 1345.34069
Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J.
9
2015
Centers on center manifolds in the Lorenz, Chen and Lü systems. Zbl 1457.34061
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
9
2014
Characterizing and computing normal forms using Lie transforms: A survey. Zbl 1001.34030
Algaba, A.; Freire, E.; Gamero, E.
8
2001
An exact homoclinic orbit and its connection with the Rössler system. Zbl 1396.37027
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
8
2015
Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Zbl 1489.37069
Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J.
8
2015
High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. Zbl 1436.34035
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
8
2020
Analytical approximation of cuspidal loops using a nonlinear time transformation method. Zbl 1433.37019
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
8
2020
Invariant curves and analytic integrability of a planar vector field. Zbl 1412.34110
Algaba, A.; García, C.; Reyes, M.
8
2019
Uniformly isochronous quintic planar vector fields. Zbl 0976.37026
Algaba, A.; Reyes, M.; Bravo, A.
7
2000
Closed curves of global bifurcations in Chua’s equation: a mechanism for their formation. Zbl 1056.37067
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J.
7
2003
Geometric criterium in the center problem. Zbl 1356.34035
Algaba, Antonio; García, Cristóbal; Giné, Jaume
7
2016
Analysis of the T-point-Hopf bifurcation in the Lorenz system. Zbl 1329.37082
Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J.
7
2015
Comment on “Sil’nikov chaos of the Liu system”. Zbl 1317.34083
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
7
2011
Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms. Zbl 1453.37045
Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
7
2020
On Darboux polynomials and rational first integrals of the generalized Lorenz system. Zbl 1302.34001
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
7
2014
Nondegenerate and nilpotent centers for a cubic system of differential equations. Zbl 1416.34020
Algaba, Antonio; García, Cristóbal; Giné, Jaume
7
2019
Isochronous centres and foci via commutators and normal forms. Zbl 1155.34018
Algaba, A.; Reyes, M.
6
2008
A degenerate Hopf-saddle-node bifurcation analysis in a family of electronic circuits. Zbl 1201.37021
Algaba, A.; Gamero, E.; García, C.; Merino, M.
6
2007
Computing simplest normal forms for the Takens-Bogdanov singularity. Zbl 1050.34052
Algaba, Antonio
6
2002
Centers with degenerate infinity and their commutators. Zbl 1037.34024
Algaba, A.; Reyes, M.
6
2003
A new algorithm for determining the monodromy of a planar differential system. Zbl 1334.34188
Algaba, A.; García, C.; Reyes, M.
6
2014
On the formal integrability problem for planar differential systems. Zbl 1282.34005
Algaba, Antonio; García, Cristóbal; Giné, Jaume
6
2013
Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. Zbl 1268.37017
Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J.
6
2012
Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\). Zbl 1267.34002
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
6
2011
Analytical integrability problem for perturbations of cubic Kolmogorov systems. Zbl 1404.37021
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
6
2018
Open-to-closed curves of saddle-node bifurcations of periodic orbits near a nontransversal T-point in Chua’s equation. Zbl 1142.34029
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J.
5
2006
Analytic integrability inside a family of degenerate centers. Zbl 1354.34005
Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume
5
2016
Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor. Zbl 1464.34006
Algaba, Antonio; García, Cristóbal; Giné, Jaume
5
2019
High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067
Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J.
5
2021
Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method. Zbl 1482.34138
Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
5
2020
Comment on ‘Šilnikov-type orbits of Lorenz-family systems’. Zbl 1395.37020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
5
2013
Analytic integrability for some degenerate planar systems. Zbl 1278.34001
Algaba, Antonio; García, Cristóbal; Giné, Jaume
5
2013
Comments on “Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces”. Zbl 1291.34080
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
5
2014
Nondegenerate centers and limit cycles of cubic Kolmogorov systems. Zbl 1390.37082
Algaba, Antonio; García, Cristóbal; Giné, Jaume
5
2018
High-order analysis of canard explosion in the Brusselator equations. Zbl 1447.34023
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
5
2020
Geometry of the uniformly isochronous centers with polynomial commutator. Zbl 1231.34052
Algaba, A.; Reyes, M.; Bravo, A.
4
2002
Hopf bifurcations and their degeneracies in Chua’s equation. Zbl 1248.34059
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J.
4
2011
Oscillation-sliding in a modified van der Pol-Duffing electronic oscillator. Zbl 1237.34049
Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
4
2002
Homoclinic connections near a Belyakov point in Chua’s equation. Zbl 1089.37019
Algaba, A.; Merino, M.; Rodríguez-Luis, A. J.
4
2005
Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system”. Zbl 1247.34072
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
4
2012
Comments on “The Chen system revisited”. Zbl 1306.34020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
4
2014
A bifurcation analysis of planar nilpotent reversible systems. Zbl 1372.34073
Algaba, A.; Freire, E.; Gamero, E.; García, C.
4
2017
Analytic integrability around a nilpotent singularity: the non-generic case. Zbl 1483.34006
Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume
4
2020
High-order study of the canard explosion in an aircraft ground dynamics model. Zbl 1459.34133
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
4
2020
A note on analytic integrability of planar vector fields. Zbl 1268.34003
Algaba, A.; García, C.; Reyes, M.
4
2012
Quasi-homogeneous linearization of degenerate vector fields. Zbl 1440.34039
Algaba, A.; García, C.; Reyes, M.
3
2020
Analytical integrability of perturbations of quadratic systems. Zbl 1481.34003
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
3
2021
Superluminal periodic orbits in the Lorenz system. Zbl 1510.34082
Algaba, A.; Merino, M.; Rodríguez-Luis, A. J.
3
2016
Homoclinic interactions near a triple-zero degeneracy in Chua’s equation. Zbl 1270.34113
Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J.
3
2012
Analysis of the T-point-Hopf bifurcation with \(\mathbb Z_2\)-symmetry. Application to Chua’s equation. Zbl 1193.34078
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
3
2010
Asymptotic expansions for a family of non-generic canards using parametric representation. Zbl 1524.34135
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
3
2020
Analytic integrability of some examples of degenerate planar vector fields. Zbl 1343.34003
Algaba, Antonio; García, Cristóbal; Giné, Jaume
2
2016
Monodromy of a class of analytic generalized nilpotent systems through their Newton diagram. Zbl 1322.34049
Algaba, A.; García, C.; Reyes, M.
2
2015
Quasi-homogeneous normal forms for null linear part. Zbl 1054.34065
Algaba, A.; Freire, E.; Gamero, E.; García, C.
2
2003
Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang. Zbl 1319.37011
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
2
2014
On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier. Zbl 1510.34074
Algaba, A.; Fuentes, N.; Gamero, E.; García, C.
2
2021
Center conditions of a particular polynomial differential system with a nilpotent singularity. Zbl 1478.34031
Algaba, Antonio; García, Cristóbal; Giné, Jaume
2
2020
Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system. Zbl 1433.34055
Algaba, A.; Fuentes, N.; Gamero, E.; García, C.
2
2020
The reversibility problem for quasi-homogeneous dynamical systems. Zbl 1283.34032
Algaba, Antonio; Gamero, Estanislao; García, Cristóbal
2
2013
Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Zbl 1277.65108
Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J.
2
2013
Center problem for generic degenerate vector fields. Zbl 1487.34088
Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume
1
2022
Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system. Zbl 1500.34016
Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J.
1
2022
High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067
Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J.
5
2021
Analytical integrability of perturbations of quadratic systems. Zbl 1481.34003
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
3
2021
On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier. Zbl 1510.34074
Algaba, A.; Fuentes, N.; Gamero, E.; García, C.
2
2021
Analytically integrable centers of perturbations of cubic homogeneous systems. Zbl 1472.34055
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
1
2021
Asymptotic expansions for a degenerate canard explosion. Zbl 1496.34094
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
1
2021
A new normal form for monodromic nilpotent singularities of planar vector fields. Zbl 1482.34106
Algaba, Antonio; García, Cristóbal; Giné, Jaume
1
2021
High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. Zbl 1436.34035
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
8
2020
Analytical approximation of cuspidal loops using a nonlinear time transformation method. Zbl 1433.37019
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
8
2020
Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms. Zbl 1453.37045
Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
7
2020
Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method. Zbl 1482.34138
Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
5
2020
High-order analysis of canard explosion in the Brusselator equations. Zbl 1447.34023
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
5
2020
Analytic integrability around a nilpotent singularity: the non-generic case. Zbl 1483.34006
Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume
4
2020
High-order study of the canard explosion in an aircraft ground dynamics model. Zbl 1459.34133
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
4
2020
Quasi-homogeneous linearization of degenerate vector fields. Zbl 1440.34039
Algaba, A.; García, C.; Reyes, M.
3
2020
Asymptotic expansions for a family of non-generic canards using parametric representation. Zbl 1524.34135
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.
3
2020
Center conditions of a particular polynomial differential system with a nilpotent singularity. Zbl 1478.34031
Algaba, Antonio; García, Cristóbal; Giné, Jaume
2
2020
Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system. Zbl 1433.34055
Algaba, A.; Fuentes, N.; Gamero, E.; García, C.
2
2020
Orbitally universal centers. Zbl 1511.34038
Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume
1
2020
A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form. Zbl 1430.37054
Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
11
2019
Analytic integrability around a nilpotent singularity. Zbl 1432.34002
Algaba, Antonio; García, Cristóbal; Giné, Jaume
10
2019
Invariant curves and analytic integrability of a planar vector field. Zbl 1412.34110
Algaba, A.; García, C.; Reyes, M.
8
2019
Nondegenerate and nilpotent centers for a cubic system of differential equations. Zbl 1416.34020
Algaba, Antonio; García, Cristóbal; Giné, Jaume
7
2019
Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor. Zbl 1464.34006
Algaba, Antonio; García, Cristóbal; Giné, Jaume
5
2019
Study of a dynamical system with a strange attractor and invariant tori. Zbl 1470.37084
Algaba, Antonio; Merino, Manuel; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.
1
2019
The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields. Zbl 1395.34047
Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume
13
2018
Analytical integrability problem for perturbations of cubic Kolmogorov systems. Zbl 1404.37021
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
6
2018
Nondegenerate centers and limit cycles of cubic Kolmogorov systems. Zbl 1390.37082
Algaba, Antonio; García, Cristóbal; Giné, Jaume
5
2018
Structural stability of planar quasi-homogeneous vector fields. Zbl 1405.34047
Algaba, A.; Fuentes, N.; Gamero, E.; Garcia, C.
2
2018
A bifurcation analysis of planar nilpotent reversible systems. Zbl 1372.34073
Algaba, A.; Freire, E.; Gamero, E.; García, C.
4
2017
Nilpotent centres via inverse integrating factors. Zbl 1384.34037
Algaba, Antonio; García, Cristóbal; Giné, Jaume
10
2016
The center problem. A view from the normal form theory. Zbl 1329.34071
Algaba, A.; Gamero, E.; García, C.
9
2016
Geometric criterium in the center problem. Zbl 1356.34035
Algaba, Antonio; García, Cristóbal; Giné, Jaume
7
2016
Analytic integrability inside a family of degenerate centers. Zbl 1354.34005
Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume
5
2016
Superluminal periodic orbits in the Lorenz system. Zbl 1510.34082
Algaba, A.; Merino, M.; Rodríguez-Luis, A. J.
3
2016
Analytic integrability of some examples of degenerate planar vector fields. Zbl 1343.34003
Algaba, Antonio; García, Cristóbal; Giné, Jaume
2
2016
On orbital-reversibility for a class of planar dynamical systems. Zbl 1337.34039
Algaba, A.; Checa, I.; García, C.; Gamero, E.
12
2015
Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Zbl 1345.34069
Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J.
9
2015
An exact homoclinic orbit and its connection with the Rössler system. Zbl 1396.37027
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
8
2015
Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Zbl 1489.37069
Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J.
8
2015
Analysis of the T-point-Hopf bifurcation in the Lorenz system. Zbl 1329.37082
Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J.
7
2015
Monodromy of a class of analytic generalized nilpotent systems through their Newton diagram. Zbl 1322.34049
Algaba, A.; García, C.; Reyes, M.
2
2015
Comments on: “Invariant algebraic surfaces of the generalized Lorenz system”. Zbl 1323.34019
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
1
2015
Analytic integrability for some degenerate planar vector fields. Zbl 1306.34046
Algaba, Antonio; García, Cristóbal; Giné, Jaume
12
2014
A class of non-integrable systems admitting an inverse integrating factor. Zbl 1333.37076
Algaba, A.; Fuentes, N.; García, C.; Reyes, M.
9
2014
Centers on center manifolds in the Lorenz, Chen and Lü systems. Zbl 1457.34061
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
9
2014
On Darboux polynomials and rational first integrals of the generalized Lorenz system. Zbl 1302.34001
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
7
2014
A new algorithm for determining the monodromy of a planar differential system. Zbl 1334.34188
Algaba, A.; García, C.; Reyes, M.
6
2014
Comments on “Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces”. Zbl 1291.34080
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
5
2014
Comments on “The Chen system revisited”. Zbl 1306.34020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
4
2014
Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang. Zbl 1319.37011
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
2
2014
Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”. Zbl 1470.37040
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
2
2014
Comment on “Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems”. Zbl 1335.37011
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
1
2014
Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system. Zbl 1323.37020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
32
2013
The Lü system is a particular case of the Lorenz system. Zbl 1301.37020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
24
2013
On the formal integrability problem for planar differential systems. Zbl 1282.34005
Algaba, Antonio; García, Cristóbal; Giné, Jaume
6
2013
Comment on ‘Šilnikov-type orbits of Lorenz-family systems’. Zbl 1395.37020
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
5
2013
Analytic integrability for some degenerate planar systems. Zbl 1278.34001
Algaba, Antonio; García, Cristóbal; Giné, Jaume
5
2013
The reversibility problem for quasi-homogeneous dynamical systems. Zbl 1283.34032
Algaba, Antonio; Gamero, Estanislao; García, Cristóbal
2
2013
Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Zbl 1277.65108
Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J.
2
2013
Centers of quasi-homogeneous polynomial planar systems. Zbl 1238.34052
Algaba, A.; Fuentes, N.; García, C.
28
2012
Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems. Zbl 1266.37023
Algaba, A.; García, C.; Reyes, M.
22
2012
Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. Zbl 1268.37017
Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J.
6
2012
Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system”. Zbl 1247.34072
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
4
2012
A note on analytic integrability of planar vector fields. Zbl 1268.34003
Algaba, A.; García, C.; Reyes, M.
4
2012
Homoclinic interactions near a triple-zero degeneracy in Chua’s equation. Zbl 1270.34113
Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J.
3
2012
Integrability of two dimensional quasi-homogeneous polynomial differential systems. Zbl 1213.37093
Algaba, A.; García, C.; Reyes, M.
24
2011
Characterization of a monodromic singular point of a planar vector field. Zbl 1226.34031
Algaba, A.; García, C.; Reyes, M.
14
2011
Comment on “Sil’nikov chaos of the Liu system”. Zbl 1317.34083
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
7
2011
Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\). Zbl 1267.34002
Algaba, Antonio; García, Cristóbal; Reyes, Manuel
6
2011
Hopf bifurcations and their degeneracies in Chua’s equation. Zbl 1248.34059
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J.
4
2011
Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems. Zbl 1192.34035
Algaba, A.; Freire, E.; Gamero, E.; García, C.
16
2010
Reversibility and quasi-homogeneous normal forms of vector fields. Zbl 1202.34069
Algaba, A.; García, C.; Teixeira, M. A.
12
2010
Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems. Zbl 1201.34050
Algaba, A.; García, C.; Reyes, M.
10
2010
Analysis of the T-point-Hopf bifurcation with \(\mathbb Z_2\)-symmetry. Application to Chua’s equation. Zbl 1193.34078
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
3
2010
The integrability problem for a class of planar systems. Zbl 1165.34023
Algaba, A.; Gamero, E.; García, C.
58
2009
Like-linearizations of vector fields. Zbl 1196.37080
Algaba, A.; García, C.; Reyes, M.
11
2009
Characterizing isochronous points and computing isochronous sections. Zbl 1208.34034
Algaba, A.; Reyes, M.
11
2009
Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations. Zbl 1201.34061
Algaba, A.; García, C.; Reyes, M.
10
2009
Degenerate global bifurcations in a simple circuit. Zbl 1187.37072
Algaba, A.; Merino, M.; García, C.; Reyes, M.
1
2009
The center problem for a family of systems of differential equations having a nilpotent singular point. Zbl 1156.34031
Algaba, A.; García, C.; Reyes, M.
25
2008
Isochronous centres and foci via commutators and normal forms. Zbl 1155.34018
Algaba, A.; Reyes, M.
6
2008
Resonances of periodic orbits in Rössler system in presence of a triple-zero bifurcation. Zbl 1145.37322
Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; Rodríguez-Luis, Alejandro J.
9
2007
A degenerate Hopf-saddle-node bifurcation analysis in a family of electronic circuits. Zbl 1201.37021
Algaba, A.; Gamero, E.; García, C.; Merino, M.
6
2007
Open-to-closed curves of saddle-node bifurcations of periodic orbits near a nontransversal T-point in Chua’s equation. Zbl 1142.34029
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J.
5
2006
A bifurcation analysis of a simple electronic circuit. Zbl 1064.34030
Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J.
11
2005
Homoclinic connections near a Belyakov point in Chua’s equation. Zbl 1089.37019
Algaba, A.; Merino, M.; Rodríguez-Luis, A. J.
4
2005
An algorithm for computing quasi-homogeneous formal normal forms under equivalence. Zbl 1063.34029
Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; García, Cristóbal
13
2004
Quasi-homogeneous normal forms. Zbl 1022.34034
Algaba, A.; Freire, E.; Gamero, E.; García, C.
28
2003
Some results on Chua’s equation near a triple-zero linear degeneracy. Zbl 1083.93020
Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
21
2003
Computing center conditions for vector fields with constant angular speed. Zbl 1032.34026
Algaba, A.; Reyes, M.
17
2003
Closed curves of global bifurcations in Chua’s equation: a mechanism for their formation. Zbl 1056.37067
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J.
7
2003
Centers with degenerate infinity and their commutators. Zbl 1037.34024
Algaba, A.; Reyes, M.
6
2003
Quasi-homogeneous normal forms for null linear part. Zbl 1054.34065
Algaba, A.; Freire, E.; Gamero, E.; García, C.
2
2003
A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. Zbl 1043.37042
Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A.
34
2002
Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations. Zbl 0999.37035
Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Merino, M.; Rodríguez-Luis, A. J.
11
2002
Computing simplest normal forms for the Takens-Bogdanov singularity. Zbl 1050.34052
Algaba, Antonio
6
2002
Geometry of the uniformly isochronous centers with polynomial commutator. Zbl 1231.34052
Algaba, A.; Reyes, M.; Bravo, A.
4
2002
Oscillation-sliding in a modified van der Pol-Duffing electronic oscillator. Zbl 1237.34049
Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.
4
2002
...and 12 more Documents
all top 5

Cited by 451 Authors

100 Algaba, Antonio
51 Rodríguez-Luis, Alejandro J.
50 García, Cristóbal
39 Giné, Jaume
29 Merino, Manuel
27 Llibre, Jaume
26 Reyes, Manuel
25 Fernández-Sánchez, Fernando
24 Freire Macías, Emilio
19 Gamero, Estanislao
17 Yu, Pei
14 García, Isaac A.
13 Qin, Bo-Wei
12 Chung, Kwok-Wai
11 Valls Anglés, Cláudia
10 Gazor, Majid
9 Li, Feng
7 Fuentes, Natalia
6 Maza, Susanna
6 Sabatini, Marco
5 Amel’kin, Vladimir Vasilievich
5 Barrio, Roberto
5 Carmona, Victoriano
5 Liang, Haihua
5 Liu, Xingbo
5 Liu, Yirong
5 Ponce, Enrique
5 Torregrosa, Joan
5 Zhang, Fuchen
4 Checa, Isabel
4 Edneral, Victor F.
4 Ferčec, Brigita
4 Han, Maoan
4 Ibáñez, Santiago
4 Itikawa, Jackson
4 Li, Chunbiao
4 Shoghi, Ahmad
4 Sprott, Julien Clinton
4 Teruel, Antonio E.
4 Wang, Duo
4 Zhang, Xiang
3 Bella, Giovanni
3 Bi, Qinsheng
3 Domínguez-Moreno, María C.
3 Drubi, Fátima
3 Fernández-García, Soledad
3 García-Medina, Elisabeth
3 Gasull, Armengol
3 Grau, Maite
3 Guo, Shangjiang
3 Huang, Wentao
3 Kapitaniak, Tomasz
3 Krauskopf, Bernd
3 Li, Jing
3 Liao, Xiaofeng
3 Liu, Xia
3 Mokhtari, Fahimeh
3 Oliveira, Regilene D. S.
3 Pessoa, Claudio
3 Rocha, Ronilson
3 Romanovskiĭ, Valeriĭ Georgievich
3 Sánchez-Sánchez, Iván
3 Serrano, Sergio E.
3 Shafer, Douglas S.
3 Tang, Yilei
3 Teixeira, Marco Antonio
3 Tian, Yuzhou
3 Wu, Yusen
3 Yang, Shuangling
3 Yuan, Yuan
3 Zhang, Guangyun
3 Zhou, Zhengxin
2 Alonso, Diego M.
2 Belhaq, Mohamed
2 Blesa, Fernando
2 Bruno, Alexander Dmitrievich
2 Buică, Adriana
2 Chen, Guanrong
2 Chen, Haibo
2 Dukarić, Maša
2 Esteban, Marina
2 García-Saldaña, Johanna D.
2 Guillamon, Antoni
2 Guo, Lina
2 Horikawa, Yo
2 Huang, Jianfeng
2 Jiang, Jiao
2 Kitajima, Hiroyuki
2 Kou, Liying
2 Kuznetsov, Yuri Alexandrovich
2 Lamb, Jeroen S. W.
2 Leung, Andrew Yee-Tak
2 Li, Shimin
2 Liu, Xuanliang
2 Liu, Yuanyuan
2 Mahdi, Adam
2 Makhlouf, Amar
2 Marwan, Muhammad
2 Mattana, Paolo
2 Meddour, Lotfi
...and 351 more Authors
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Cited in 87 Serials

72 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
32 Journal of Differential Equations
23 Journal of Mathematical Analysis and Applications
21 Qualitative Theory of Dynamical Systems
18 Chaos, Solitons and Fractals
17 Nonlinear Dynamics
15 Physica D
13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
13 Communications in Nonlinear Science and Numerical Simulation
12 Applied Mathematics and Computation
11 Chaos
10 Nonlinear Analysis. Real World Applications
7 Journal of Computational and Applied Mathematics
7 Differential Equations
6 Physics Letters. A
6 Bulletin des Sciences Mathématiques
6 Discrete and Continuous Dynamical Systems
5 Applied Mathematics Letters
5 Discrete and Continuous Dynamical Systems. Series B
5 SIAM Journal on Applied Dynamical Systems
4 Journal of Symbolic Computation
4 Abstract and Applied Analysis
4 Advances in Difference Equations
4 Journal of Applied Analysis and Computation
3 Mathematical Methods in the Applied Sciences
3 Journal of Dynamical and Control Systems
3 Mediterranean Journal of Mathematics
2 Nonlinearity
2 Rocky Mountain Journal of Mathematics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Mathematics and Computers in Simulation
2 Proceedings of the American Mathematical Society
2 Systems & Control Letters
2 Applied Mathematics and Mechanics. (English Edition)
2 Acta Applicandae Mathematicae
2 European Journal of Applied Mathematics
2 Applied Mathematical Modelling
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Journal of Dynamics and Differential Equations
2 Journal of Nonlinear Science
2 Acta Mathematica Sinica. English Series
2 Communications in Contemporary Mathematics
2 Dynamical Systems
2 Journal of Applied Mathematics
2 AIMS Mathematics
1 Computers & Mathematics with Applications
1 Communications in Mathematical Physics
1 Journal of Statistical Physics
1 Periodica Mathematica Hungarica
1 Physica A
1 Advances in Mathematics
1 Automatica
1 Collectanea Mathematica
1 Numerische Mathematik
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Ergodic Theory and Dynamical Systems
1 Chinese Annals of Mathematics. Series B
1 Revista Matemática Iberoamericana
1 Dynamics and Stability of Systems
1 Neural Computation
1 Economics Letters
1 Journal of Mathematical Sciences (New York)
1 Electronic Journal of Differential Equations (EJDE)
1 Computational and Applied Mathematics
1 Journal of Difference Equations and Applications
1 Journal of Mathematical Chemistry
1 Soft Computing
1 Discrete Dynamics in Nature and Society
1 New Journal of Physics
1 Journal of Nonlinear Mathematical Physics
1 Nonlinear Analysis. Modelling and Control
1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms
1 Journal of Systems Science and Complexity
1 Nonlinear Dynamics and Systems Theory
1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
1 Communications on Pure and Applied Analysis
1 Journal of Dynamical Systems and Geometric Theories
1 Bulletin of the Brazilian Mathematical Society. New Series
1 Journal of Statistical Mechanics: Theory and Experiment
1 Mathematical Biosciences and Engineering
1 Advances in Mathematical Physics
1 Malaysian Journal of Mathematical Sciences
1 Advances in Nonlinear Analysis
1 Journal of Mathematics
1 European Journal of Mathematics
1 International Journal of Applied and Computational Mathematics
1 Bollettino dell’Unione Matematica Italiana

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