Edit Profile (opens in new tab) Algaba, Antonio Co-Author Distance Author ID: algaba.antonio Published as: Algaba, Antonio; Algaba, A. Documents Indexed: 128 Publications since 1998, including 1 Additional arXiv Preprint Co-Authors: 18 Co-Authors with 127 Joint Publications 514 Co-Co-Authors all top 5 Co-Authors 1 single-authored 61 García, Cristóbal 55 Rodríguez-Luis, Alejandro J. 36 Merino, Manuel 32 Gamero, Estanislao 31 Reyes, Manuel 23 Freire Macías, Emilio 22 Fernández-Sánchez, Fernando 19 Giné, Jaume 12 Qin, Bo-Wei 11 Chung, Kwok-Wai 7 Fuentes, Natalia 4 Checa, Isabel 4 Domínguez-Moreno, María C. 2 Díaz, Maria Elena 2 Llibre, Jaume 1 Maestre, Manuel 1 Ponce, Enrique 1 Teixeira, Marco Antonio 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 all top 5 Fields 110 Ordinary differential equations (34-XX) 62 Dynamical systems and ergodic theory (37-XX) 5 Mechanics of particles and systems (70-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Nonassociative rings and algebras (17-XX) 1 Approximations and expansions (41-XX) 1 Numerical analysis (65-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 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. 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