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Author ID: mira.christian Recent zbMATH articles by "Mira, Christian"
Published as: Mira, Christian; Mira, C.; Mira, Ch.

Publications by Year

Citations contained in zbMATH Open

96 Publications have been cited 848 times in 413 Documents Cited by Year
Chaotic dynamics in two-dimensional noninvertible maps. Zbl 0906.58027
Mira, Christian; Gardini, Laura; Barugola, Alexandra; Cathala, Jean-Claude
145
1996
Chaotic dynamics. From the one-dimensional endomorphism to the two- dimensional diffeomorphism. Zbl 0641.58002
Mira, Christian
55
1987
Basin bifurcations of two-dimensional noninvertible maps: Fractalization of basins. Zbl 0818.58032
Mira, C.; Fournier-Prunaret, D.; Gardini, L.; Kawakami, H.; Cathala, J. C.
45
1994
Recurrences and discrete dynamic systems. Zbl 0449.58003
Gumowski, Igor; Mira, Christian
45
1980
Dynamique chaotique. Transformations ponctuelles. Transition. Ordre - desordre. Zbl 0442.93001
Gumowski, I.; Mira, C.
40
1980
Plane maps with denominator. I: Some generic properties. Zbl 0996.37052
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
37
1999
On some properties of invariant sets of two-dimensional noninvertible maps. Zbl 0905.58016
Frouzakis, Christos E.; Gardini, Laura; Kevrekidis, Ioannis G.; Millerioux, Gilles; Mira, Christian
29
1997
Plane maps with denominator. II: Noninvertible maps with simple focal points. Zbl 1057.37042
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
19
2003
“Crossroad area – spring area” transition. I: Parameter plane representation. Zbl 0758.58025
Carcasses, J. P.; Mira, C.; Bosch, M.; Simó, C.; Tatjer, J. C.
18
1991
On behaviors of two-dimensional endomorphisms: Role of the critical curves. Zbl 0870.58079
Mira, Christian; Narayaninsamy, Tony
17
1993
Complex dynamics in two-dimensional endomorphisms. Zbl 0462.58021
Mira, C.
17
1980
Chaos in discrete dynamical systems: a visual introduction in 2 dimensions. Companion CD-ROM by Ronald J. Record and Ralph H. Abraham. Zbl 0883.58019
Abraham, Ralph H.; Gardini, Laura; Mira, Christian
16
1997
Plane maps with denominator . Part III: Nonsimple focal points and related bifurcations. Zbl 1082.37042
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
15
2005
On the “crossroad area-saddle area” and “crossroad area-spring area” transitions. Zbl 0874.58060
Mira, C.; Carcassès, J. P.
11
1991
Optimization in control theory and practice. Zbl 0242.49002
Gumowski, I.; Mira, C.
11
1968
Annular chaotic areas. Zbl 0617.58024
Barugola, A.; Cathala, J. C.; Mira, C.
10
1986
Embedding of a Dim1 piecewise continuous and linear Leonov map into a Dim2 invertible map. Zbl 1296.37033
Mira, Christian
9
2013
“Crossroad area – spring area” transition. II: Foliated parametric representation. Zbl 0876.58035
Mira, C.; Carcassès, J. P.; Bosch, M.; Simó, C.; Tatjer, J. C.
9
1991
Sur la structure des bifurcations des difféomorphismes du cercle. Zbl 0396.58018
Mira, Christian
9
1978
Cas ou le domaine de stabilité d’un ensemble limite attractif d’une recurrence du deuxième ordre n’est pas simplement connexe. Zbl 0179.22004
Mira, C.; Roubellat, F.
9
1969
Unbounded sets of attraction. Zbl 1090.37511
Bischi, Gian-Italo; Mira, Christian; Gardini, Laura
8
2000
Finite-time global chaos synchronization for piecewise linear maps. Zbl 1011.37059
Millerioux, Gilles; Mira, Christian
8
2001
Singular points with two multipliers, \(S_ 1=-S_ 2=1\), in the bifurcation curves of maps. Zbl 0874.58056
Cathala, J. C.; Kawakami, H.; Mira, C.
8
1992
Lien entre des propriétés d’un endomorphisme de dimension un et celles d’un difféomorphisme de dimension deux. Zbl 0482.58025
Hamouly, Hassan El; Mira, Christian
8
1981
Sensitivity problems related to certain bifurcations in non-linear recurrence relations. Zbl 0185.18203
Gumowski, I.; Mira, C.
8
1969
Solutions “chaotiques” bornees d’une recurrence, ou transformation ponctuelle du deuxième ordre, à inverse non unique. Zbl 0354.93037
Gumowski, Igor; Mira, Christian
8
1977
From the box-within-a-box bifurcation organization to the Julia set. I: Revisited properties of the sets generated by a quadratic complex map with a real parameter. Zbl 1170.37323
Mira, Christian; Gardini, Laura
7
2009
Invariant curves and focal points in a Lyness iterative process. Zbl 1063.39016
Gardini, L.; Bischi, G. I.; Mira, C.
7
2003
Extensions of the notion of chaotic area in second-order endomorphisms. Zbl 0885.58044
Barugola, A.; Cathala, J. C.; Mira, C.
7
1995
Coding scheme based on chaos synchronization from noninvertible maps. Zbl 1002.94029
Millerioux, G.; Mira, C.
7
1998
Bifurcation destabilisant une solution chaotique d’un endomorphisme du deuxième ordre. Zbl 0369.93032
Gumowski, Igor; Mira, Christian
7
1978
Some properties of a two-dimensional piecewise-linear noninvertible map. Zbl 1298.37019
Mira, Christian; Rauzy, Christine; Maistrenko, Yuri; Sushko, Irina
6
1996
Bifurcation structures generated by the nonautonomous Duffing equation. Zbl 0970.34031
Mira, C.; Touzani-Qriouet, M.; Kawakami, H.
6
1999
“Crossroad area – dissymmetrical spring area – symmetrical spring area”, and “double crossroad area – double spring area” transitions. Zbl 0870.58075
Allam, Rezk; Mira, Christian
6
1993
Plane foliation of two-dimensional noninvertible maps. Zbl 0879.58063
Mira, Christian; Carcasses, Jean-Pierre; Millérioux, Gilles; Gardini, Laura
6
1996
Fractal aggregation of basin islands in two-dimensional quadratic noninvertible maps. Zbl 0886.58070
Mira, C.; Rauzy, C.
6
1995
On a “crossroad area-spring area” transition occuring in a Duffing-Rayleigh equation with a periodical excitation. Zbl 0896.34029
Mira, Christian; Qriouet, Mohammed
6
1993
Accumulations de bifurcations dans une recurrence. Zbl 0323.26002
Gumowski, Igor; Mira, Christian
6
1975
Sur l’itération fractionnaire d’un endomorphisme quadratique. Zbl 0546.58012
Mira, Christian; Müllenbach, Sabine
6
1983
Maps with a vanishing denominator. A survey of some results. Zbl 1042.37515
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
6
2001
Bifurcation structure in a model of a frequency modulated \(\text{CO}_ 2\) laser. Zbl 0873.34024
Mira, C.; Djellit, I.
5
1993
Some contact bifurcations in two-dimensional examples. Zbl 0930.37038
Fournier-Prunaret, Danièle; Mira, Christian; Gardini, Laura
5
1997
Some historical aspects of nonlinear dynamics: Possible trends for the future. Zbl 0914.34004
Mira, Christian
5
1997
On the fractal structure of basin boundaries in two-dimensional noninvertible maps. Zbl 1056.37058
Agliari, A.; Gardini, L.; Mira, C.
5
2003
On the embedding of a \((p-1)\)-dimensional noninvertible map into a \(p\)-dimensional invertible map \((p=2,3)\). Zbl 1056.37021
Mira, Christian; Gracio, Clara
5
2003
The dovetail bifurcation structure and its qualitative changes. Zbl 0894.58053
Mira, C.; Kawakami, H.; Allam, R.
5
1993
Singularites dues au feuilletage du plan des bifurcations d’un difféomorphisme bi-dimensionnel. Zbl 0513.58035
El Hamouly, Hassan; Mira, Christian
5
1982
Quelques exemples de solutions stochastiques bornees dans les recurrences autonomes du \(2^e\) ordre. Zbl 0368.65061
Bernussou, J.; Hsu, Liu; Mira, C.
5
1976
Basin fractalizations generated by a two-dimensional family of \((Z_1-Z_3-Z_1)\) maps. Zbl 1141.37337
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
4
2006
Slow-fast dynamics generated by noninvertible plane maps. Zbl 1096.37022
Mira, Christian; Shilnikov, Andrey
4
2005
Fractional harmonic synchronization in the Duffing-Rayleigh differential equation. Zbl 0811.34027
Qriouet, M.; Mira, C.
4
1994
Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0912.34036
Mira, Christian
4
1997
Contact bifurcations of absorbing areas and chaotic areas in two-dimensional endomorphisms. Zbl 0919.58050
Gardini, L.; Cathala, J. C.; Mira, C.
4
1996
Properties of invariant areas in two-dimensional endomorphisms. Zbl 0917.58040
Gardini, Laura; Mira, Christian; Fournier-Prunaret, Daniele
4
1996
Chaos and fractal properties induced by noninvertibility of models in the form of maps. Zbl 1160.37332
Mira, Christian
4
2000
Homoclinic and heteroclinic situations specific to two-dimensional noninvertible maps. Zbl 0890.58062
Millerioux, Gilles; Mira, Christian
4
1997
Noninvertible piecewise linear maps applied to chaos synchronization and secure communications. Zbl 0899.58041
Millerioux, G.; Mira, C.
4
1997
Stochastic solutions in a conservative dynamic system. Zbl 0281.34020
Gumowski, I.; Mira, C.
4
1973
Sur quelques propriétés de la frontière du domaine de stabilité d’un point double d’une recurrence du deuxième ordre à variables réelles et sur un cas de bifurcation de cette frontière. Zbl 0171.36602
Mira, C.
4
1966
Reducible fractional harmonics generated by the nonautonomous Duffing-Rayleigh equation. Pockets of reducible harmonics and Arnold’s tongues. Zbl 1090.34550
Qriouet, M. Touzani; Mira, C.
3
2000
A method to calculate basin bifurcation sets for a two-dimensional noninvertible map. Zbl 1090.37544
Kitajima, H.; Kawakami, H.; Mira, C.
3
2000
Behavior of harmonics generated by a Duffing type equation with a nonlinear damping. I. Zbl 1093.70506
Khammari, Hédi; Mira, Christian; Carcassés, Jean-Pierre
3
2005
Séquences de Myrberg et communications entre feuillets du plan des bifurcations d’un difféomorphisme bi-dimensionnel. (Myrberg’s sequences and communications between the sheets of the bifurcation plane of a bi- dimensional diffeomorphism). Zbl 0603.58014
Fournier, Danielle; Kawakami, Hiroshi; Mira, Christian
3
1985
Frontière floue séparant les domaines d’attraction de deux attracteurs. Zbl 0397.34063
Mira, Christian
3
1979
Accumulations de bifurcations et ”structures boites emboitees” dans les recurrences et transformations ponctuelles. Zbl 0414.34015
Mira, Christian
3
1977
Equation de Schroeder et solution des recurrences. Généralisation des polynômes de Tchebycheff. Zbl 0519.58043
Mira, Ch.
3
1982
Sur les cas d’exception d’une récurrence ou une transformation ponctuelle autonome, du deuxième ordre à variables réelles. Zbl 0208.40604
Mira, C.
3
1970
Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0886.58050
Mira, Christian
3
1997
Sur la frontière du domaine de stabilité d’un point double d’une recurrence non linéaire, lorsque cette frontière ne contient pas de point double. Zbl 0189.48005
Gumowski, I.; Mira, C.; Riberi, E.
2
1967
Étude d’un second cas d’exception pour une récurrence, ou une transformation ponctuelle, autonome du deuxième ordre, à variables réelles. Zbl 0208.40603
Mira, C.
2
1970
Bifurcation pour une recurrence du deuxième ordre, par traversee d’un cas critique avec deux multiplicateurs complexes conjugues. Zbl 0284.39003
Gumowski, Igor; Mira, Christian
2
1974
Sur les recurrences, ou transformations ponctuelles, du premier ordre, avec inverse non unique. Zbl 0303.65100
Gumowski, Igor; Mira, Christian
2
1975
Sur les bifurcations d’un difféomorphisme quadratique bi-dimensionnel. Situations homoclines et hétéroclines. Zone Morse-Smale. (Bifurcations of a quadratic two-dimensional diffeomorphism, homoclinic and heteroclinic situations. Morse-Smale area). Zbl 0557.34039
Fournier, Danielle; Kawakami, Hiroshi; Mira, Christian
2
1984
Nonlinear control systems. (Systèmes asservis non linéaires.) Zbl 0864.93008
Mira, Christian
2
1990
Rotation sequences and bifurcations structure of one-dimensional endomorphisms. Zbl 0611.58032
Mira, Christian
1
1985
Isoordinal cascade of cusps with monotonic convergence in a bifurcation plane, generated by a two-dimensional diffeomorphism. Zbl 1026.37515
Mira, Christian; Taha, Abdel-Kaddous
1
1991
An autonomous ordinary differential equation generating alternating isoordinal cascades of cusps in a bifurcation plane. Zbl 1026.37516
Carcassès, Jean-Pierre; Mira, Christian
1
1991
Implicit approximation of a stable saddle manifold generated by a two-dimensional quadratic map. Zbl 1192.37073
Mira, Christian; Abdel-Baset, Heba; El-Hamouly, Hassan
1
1999
Contact bifurcations related to critical sets and focal points in iterated maps of the plane. Zbl 1242.39024
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
1
2011
From the box-within-a-box bifurcation structure to the Julia set. II: Bifurcation routes to different Julia sets from an indirect embedding of a quadratic complex map. Zbl 1182.37032
Mira, Christian; Agliari, Anna; Gardini, Laura
1
2009
Systemes à dynamique complexe et bifurcations de type ”boites emboitees” cas des recurrences d’ordre 1 déterminees par une fonction à un seul extremum. Zbl 0394.93018
Mira, C.
1
1978
Systemes à dynamique complexe et bifurcations de type ”boites emboitees” cas des recurrences d’ordre 1 déterminees par une fonction à un seul extremum. II. Cas général. Zbl 0405.93016
Mira, C.
1
1978
Dynamique complexe engendree par une équation différentielle d’ordre 3. Zbl 0435.34036
Mira, C.
1
1978
Sur une méthode de détermination des exposants caractéristiques d’un système d’équations différentielles linéaires à coefficients périodiques. Zbl 0245.34005
Burgat, Christian; Mira, Christian
1
1970
Cas critique d’une recurrence, ou d’une transformation ponctuelle, du quatrieme ordre avec multiplicateurs complexes. Zbl 0262.65076
Mira, Christian
1
1971
Sur la distribution des cycles d’une recurrence ou transformation ponctuelle, conservative du deuxième ordre. Zbl 0278.65122
Gumowski, Igor; Mira, Christian
1
1972
Structures de bifurcation ’boites emboitees’ dans les recurrences, ou transformations ponctuelles du premier ordre, dont la fonction presente un seul extremum. Application à un problème de ’chaos’ en biologie. Zbl 0351.92003
Mira, Christian
1
1976
Étude d’un modèle de croissance d’une population biologique en l’absence de recouvrement de generations. Zbl 0351.92004
Mira, Christian
1
1976
Stochastic solutions in a conservative dynamic system. Zbl 0355.34032
Gumowski, I.; Mira, C.
1
1973
Two applications of noninvertible maps in communication and information storage. Zbl 1001.90009
Mira, C.; Millérioux, G.; Rouabhi, S.
1
2002
Extension des notions de points singuliers aux équations aux différences. Zbl 0116.29101
Mira, C.
1
1963
Étude d’un cas critique pour des recurrences du deuxième ordre. Zbl 0155.12401
Mira, C.; Roubellat, F.
1
1968
Sur un cas critique pour une recurrence autonome du deuxième ordre. Zbl 0167.38802
Babary, J.-P.; Mira, C.
1
1969
Traversee d’un cas critique, pour une recurrence du deuxième ordre, sous l’effet d’une variation de paramètre. Zbl 0169.42602
Mira, C.
1
1969
Étude de la traversee d’un cas critique, pour une recurrence du deuxième ordre sous l’effet d’une variation de paramètre. Zbl 0172.19105
Mira, C.; Roubellat, F.
1
1968
Sur la double interpretation, déterministe et statistique, de certaines bifurcations complexes. Zbl 0377.65063
Mira, Christian
1
1976
Embedding of a Dim1 piecewise continuous and linear Leonov map into a Dim2 invertible map. Zbl 1296.37033
Mira, Christian
9
2013
Contact bifurcations related to critical sets and focal points in iterated maps of the plane. Zbl 1242.39024
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
1
2011
From the box-within-a-box bifurcation organization to the Julia set. I: Revisited properties of the sets generated by a quadratic complex map with a real parameter. Zbl 1170.37323
Mira, Christian; Gardini, Laura
7
2009
From the box-within-a-box bifurcation structure to the Julia set. II: Bifurcation routes to different Julia sets from an indirect embedding of a quadratic complex map. Zbl 1182.37032
Mira, Christian; Agliari, Anna; Gardini, Laura
1
2009
Basin fractalizations generated by a two-dimensional family of \((Z_1-Z_3-Z_1)\) maps. Zbl 1141.37337
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
4
2006
Plane maps with denominator . Part III: Nonsimple focal points and related bifurcations. Zbl 1082.37042
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
15
2005
Slow-fast dynamics generated by noninvertible plane maps. Zbl 1096.37022
Mira, Christian; Shilnikov, Andrey
4
2005
Behavior of harmonics generated by a Duffing type equation with a nonlinear damping. I. Zbl 1093.70506
Khammari, Hédi; Mira, Christian; Carcassés, Jean-Pierre
3
2005
Plane maps with denominator. II: Noninvertible maps with simple focal points. Zbl 1057.37042
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
19
2003
Invariant curves and focal points in a Lyness iterative process. Zbl 1063.39016
Gardini, L.; Bischi, G. I.; Mira, C.
7
2003
On the fractal structure of basin boundaries in two-dimensional noninvertible maps. Zbl 1056.37058
Agliari, A.; Gardini, L.; Mira, C.
5
2003
On the embedding of a \((p-1)\)-dimensional noninvertible map into a \(p\)-dimensional invertible map \((p=2,3)\). Zbl 1056.37021
Mira, Christian; Gracio, Clara
5
2003
Two applications of noninvertible maps in communication and information storage. Zbl 1001.90009
Mira, C.; Millérioux, G.; Rouabhi, S.
1
2002
Finite-time global chaos synchronization for piecewise linear maps. Zbl 1011.37059
Millerioux, Gilles; Mira, Christian
8
2001
Maps with a vanishing denominator. A survey of some results. Zbl 1042.37515
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
6
2001
Unbounded sets of attraction. Zbl 1090.37511
Bischi, Gian-Italo; Mira, Christian; Gardini, Laura
8
2000
Chaos and fractal properties induced by noninvertibility of models in the form of maps. Zbl 1160.37332
Mira, Christian
4
2000
Reducible fractional harmonics generated by the nonautonomous Duffing-Rayleigh equation. Pockets of reducible harmonics and Arnold’s tongues. Zbl 1090.34550
Qriouet, M. Touzani; Mira, C.
3
2000
A method to calculate basin bifurcation sets for a two-dimensional noninvertible map. Zbl 1090.37544
Kitajima, H.; Kawakami, H.; Mira, C.
3
2000
Plane maps with denominator. I: Some generic properties. Zbl 0996.37052
Bischi, Gian-Italo; Gardini, Laura; Mira, Christian
37
1999
Bifurcation structures generated by the nonautonomous Duffing equation. Zbl 0970.34031
Mira, C.; Touzani-Qriouet, M.; Kawakami, H.
6
1999
Implicit approximation of a stable saddle manifold generated by a two-dimensional quadratic map. Zbl 1192.37073
Mira, Christian; Abdel-Baset, Heba; El-Hamouly, Hassan
1
1999
Coding scheme based on chaos synchronization from noninvertible maps. Zbl 1002.94029
Millerioux, G.; Mira, C.
7
1998
On some properties of invariant sets of two-dimensional noninvertible maps. Zbl 0905.58016
Frouzakis, Christos E.; Gardini, Laura; Kevrekidis, Ioannis G.; Millerioux, Gilles; Mira, Christian
29
1997
Chaos in discrete dynamical systems: a visual introduction in 2 dimensions. Companion CD-ROM by Ronald J. Record and Ralph H. Abraham. Zbl 0883.58019
Abraham, Ralph H.; Gardini, Laura; Mira, Christian
16
1997
Some contact bifurcations in two-dimensional examples. Zbl 0930.37038
Fournier-Prunaret, Danièle; Mira, Christian; Gardini, Laura
5
1997
Some historical aspects of nonlinear dynamics: Possible trends for the future. Zbl 0914.34004
Mira, Christian
5
1997
Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0912.34036
Mira, Christian
4
1997
Homoclinic and heteroclinic situations specific to two-dimensional noninvertible maps. Zbl 0890.58062
Millerioux, Gilles; Mira, Christian
4
1997
Noninvertible piecewise linear maps applied to chaos synchronization and secure communications. Zbl 0899.58041
Millerioux, G.; Mira, C.
4
1997
Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0886.58050
Mira, Christian
3
1997
Chaotic dynamics in two-dimensional noninvertible maps. Zbl 0906.58027
Mira, Christian; Gardini, Laura; Barugola, Alexandra; Cathala, Jean-Claude
145
1996
Some properties of a two-dimensional piecewise-linear noninvertible map. Zbl 1298.37019
Mira, Christian; Rauzy, Christine; Maistrenko, Yuri; Sushko, Irina
6
1996
Plane foliation of two-dimensional noninvertible maps. Zbl 0879.58063
Mira, Christian; Carcasses, Jean-Pierre; Millérioux, Gilles; Gardini, Laura
6
1996
Contact bifurcations of absorbing areas and chaotic areas in two-dimensional endomorphisms. Zbl 0919.58050
Gardini, L.; Cathala, J. C.; Mira, C.
4
1996
Properties of invariant areas in two-dimensional endomorphisms. Zbl 0917.58040
Gardini, Laura; Mira, Christian; Fournier-Prunaret, Daniele
4
1996
Extensions of the notion of chaotic area in second-order endomorphisms. Zbl 0885.58044
Barugola, A.; Cathala, J. C.; Mira, C.
7
1995
Fractal aggregation of basin islands in two-dimensional quadratic noninvertible maps. Zbl 0886.58070
Mira, C.; Rauzy, C.
6
1995
Basin bifurcations of two-dimensional noninvertible maps: Fractalization of basins. Zbl 0818.58032
Mira, C.; Fournier-Prunaret, D.; Gardini, L.; Kawakami, H.; Cathala, J. C.
45
1994
Fractional harmonic synchronization in the Duffing-Rayleigh differential equation. Zbl 0811.34027
Qriouet, M.; Mira, C.
4
1994
On behaviors of two-dimensional endomorphisms: Role of the critical curves. Zbl 0870.58079
Mira, Christian; Narayaninsamy, Tony
17
1993
“Crossroad area – dissymmetrical spring area – symmetrical spring area”, and “double crossroad area – double spring area” transitions. Zbl 0870.58075
Allam, Rezk; Mira, Christian
6
1993
On a “crossroad area-spring area” transition occuring in a Duffing-Rayleigh equation with a periodical excitation. Zbl 0896.34029
Mira, Christian; Qriouet, Mohammed
6
1993
Bifurcation structure in a model of a frequency modulated \(\text{CO}_ 2\) laser. Zbl 0873.34024
Mira, C.; Djellit, I.
5
1993
The dovetail bifurcation structure and its qualitative changes. Zbl 0894.58053
Mira, C.; Kawakami, H.; Allam, R.
5
1993
Singular points with two multipliers, \(S_ 1=-S_ 2=1\), in the bifurcation curves of maps. Zbl 0874.58056
Cathala, J. C.; Kawakami, H.; Mira, C.
8
1992
“Crossroad area – spring area” transition. I: Parameter plane representation. Zbl 0758.58025
Carcasses, J. P.; Mira, C.; Bosch, M.; Simó, C.; Tatjer, J. C.
18
1991
On the “crossroad area-saddle area” and “crossroad area-spring area” transitions. Zbl 0874.58060
Mira, C.; Carcassès, J. P.
11
1991
“Crossroad area – spring area” transition. II: Foliated parametric representation. Zbl 0876.58035
Mira, C.; Carcassès, J. P.; Bosch, M.; Simó, C.; Tatjer, J. C.
9
1991
Isoordinal cascade of cusps with monotonic convergence in a bifurcation plane, generated by a two-dimensional diffeomorphism. Zbl 1026.37515
Mira, Christian; Taha, Abdel-Kaddous
1
1991
An autonomous ordinary differential equation generating alternating isoordinal cascades of cusps in a bifurcation plane. Zbl 1026.37516
Carcassès, Jean-Pierre; Mira, Christian
1
1991
Nonlinear control systems. (Systèmes asservis non linéaires.) Zbl 0864.93008
Mira, Christian
2
1990
Chaotic dynamics. From the one-dimensional endomorphism to the two- dimensional diffeomorphism. Zbl 0641.58002
Mira, Christian
55
1987
Annular chaotic areas. Zbl 0617.58024
Barugola, A.; Cathala, J. C.; Mira, C.
10
1986
Séquences de Myrberg et communications entre feuillets du plan des bifurcations d’un difféomorphisme bi-dimensionnel. (Myrberg’s sequences and communications between the sheets of the bifurcation plane of a bi- dimensional diffeomorphism). Zbl 0603.58014
Fournier, Danielle; Kawakami, Hiroshi; Mira, Christian
3
1985
Rotation sequences and bifurcations structure of one-dimensional endomorphisms. Zbl 0611.58032
Mira, Christian
1
1985
Sur les bifurcations d’un difféomorphisme quadratique bi-dimensionnel. Situations homoclines et hétéroclines. Zone Morse-Smale. (Bifurcations of a quadratic two-dimensional diffeomorphism, homoclinic and heteroclinic situations. Morse-Smale area). Zbl 0557.34039
Fournier, Danielle; Kawakami, Hiroshi; Mira, Christian
2
1984
Sur l’itération fractionnaire d’un endomorphisme quadratique. Zbl 0546.58012
Mira, Christian; Müllenbach, Sabine
6
1983
Singularites dues au feuilletage du plan des bifurcations d’un difféomorphisme bi-dimensionnel. Zbl 0513.58035
El Hamouly, Hassan; Mira, Christian
5
1982
Equation de Schroeder et solution des recurrences. Généralisation des polynômes de Tchebycheff. Zbl 0519.58043
Mira, Ch.
3
1982
Lien entre des propriétés d’un endomorphisme de dimension un et celles d’un difféomorphisme de dimension deux. Zbl 0482.58025
Hamouly, Hassan El; Mira, Christian
8
1981
Recurrences and discrete dynamic systems. Zbl 0449.58003
Gumowski, Igor; Mira, Christian
45
1980
Dynamique chaotique. Transformations ponctuelles. Transition. Ordre - desordre. Zbl 0442.93001
Gumowski, I.; Mira, C.
40
1980
Complex dynamics in two-dimensional endomorphisms. Zbl 0462.58021
Mira, C.
17
1980
Frontière floue séparant les domaines d’attraction de deux attracteurs. Zbl 0397.34063
Mira, Christian
3
1979
Sur la structure des bifurcations des difféomorphismes du cercle. Zbl 0396.58018
Mira, Christian
9
1978
Bifurcation destabilisant une solution chaotique d’un endomorphisme du deuxième ordre. Zbl 0369.93032
Gumowski, Igor; Mira, Christian
7
1978
Systemes à dynamique complexe et bifurcations de type ”boites emboitees” cas des recurrences d’ordre 1 déterminees par une fonction à un seul extremum. Zbl 0394.93018
Mira, C.
1
1978
Systemes à dynamique complexe et bifurcations de type ”boites emboitees” cas des recurrences d’ordre 1 déterminees par une fonction à un seul extremum. II. Cas général. Zbl 0405.93016
Mira, C.
1
1978
Dynamique complexe engendree par une équation différentielle d’ordre 3. Zbl 0435.34036
Mira, C.
1
1978
Solutions “chaotiques” bornees d’une recurrence, ou transformation ponctuelle du deuxième ordre, à inverse non unique. Zbl 0354.93037
Gumowski, Igor; Mira, Christian
8
1977
Accumulations de bifurcations et ”structures boites emboitees” dans les recurrences et transformations ponctuelles. Zbl 0414.34015
Mira, Christian
3
1977
Quelques exemples de solutions stochastiques bornees dans les recurrences autonomes du \(2^e\) ordre. Zbl 0368.65061
Bernussou, J.; Hsu, Liu; Mira, C.
5
1976
Structures de bifurcation ’boites emboitees’ dans les recurrences, ou transformations ponctuelles du premier ordre, dont la fonction presente un seul extremum. Application à un problème de ’chaos’ en biologie. Zbl 0351.92003
Mira, Christian
1
1976
Étude d’un modèle de croissance d’une population biologique en l’absence de recouvrement de generations. Zbl 0351.92004
Mira, Christian
1
1976
Sur la double interpretation, déterministe et statistique, de certaines bifurcations complexes. Zbl 0377.65063
Mira, Christian
1
1976
Accumulations de bifurcations dans une recurrence. Zbl 0323.26002
Gumowski, Igor; Mira, Christian
6
1975
Sur les recurrences, ou transformations ponctuelles, du premier ordre, avec inverse non unique. Zbl 0303.65100
Gumowski, Igor; Mira, Christian
2
1975
Bifurcation pour une recurrence du deuxième ordre, par traversee d’un cas critique avec deux multiplicateurs complexes conjugues. Zbl 0284.39003
Gumowski, Igor; Mira, Christian
2
1974
Stochastic solutions in a conservative dynamic system. Zbl 0281.34020
Gumowski, I.; Mira, C.
4
1973
Stochastic solutions in a conservative dynamic system. Zbl 0355.34032
Gumowski, I.; Mira, C.
1
1973
Sur la distribution des cycles d’une recurrence ou transformation ponctuelle, conservative du deuxième ordre. Zbl 0278.65122
Gumowski, Igor; Mira, Christian
1
1972
Cas critique d’une recurrence, ou d’une transformation ponctuelle, du quatrieme ordre avec multiplicateurs complexes. Zbl 0262.65076
Mira, Christian
1
1971
Sur les cas d’exception d’une récurrence ou une transformation ponctuelle autonome, du deuxième ordre à variables réelles. Zbl 0208.40604
Mira, C.
3
1970
Étude d’un second cas d’exception pour une récurrence, ou une transformation ponctuelle, autonome du deuxième ordre, à variables réelles. Zbl 0208.40603
Mira, C.
2
1970
Sur une méthode de détermination des exposants caractéristiques d’un système d’équations différentielles linéaires à coefficients périodiques. Zbl 0245.34005
Burgat, Christian; Mira, Christian
1
1970
Cas ou le domaine de stabilité d’un ensemble limite attractif d’une recurrence du deuxième ordre n’est pas simplement connexe. Zbl 0179.22004
Mira, C.; Roubellat, F.
9
1969
Sensitivity problems related to certain bifurcations in non-linear recurrence relations. Zbl 0185.18203
Gumowski, I.; Mira, C.
8
1969
Sur un cas critique pour une recurrence autonome du deuxième ordre. Zbl 0167.38802
Babary, J.-P.; Mira, C.
1
1969
Traversee d’un cas critique, pour une recurrence du deuxième ordre, sous l’effet d’une variation de paramètre. Zbl 0169.42602
Mira, C.
1
1969
Optimization in control theory and practice. Zbl 0242.49002
Gumowski, I.; Mira, C.
11
1968
Étude d’un cas critique pour des recurrences du deuxième ordre. Zbl 0155.12401
Mira, C.; Roubellat, F.
1
1968
Étude de la traversee d’un cas critique, pour une recurrence du deuxième ordre sous l’effet d’une variation de paramètre. Zbl 0172.19105
Mira, C.; Roubellat, F.
1
1968
Sur la frontière du domaine de stabilité d’un point double d’une recurrence non linéaire, lorsque cette frontière ne contient pas de point double. Zbl 0189.48005
Gumowski, I.; Mira, C.; Riberi, E.
2
1967
Sur quelques propriétés de la frontière du domaine de stabilité d’un point double d’une recurrence du deuxième ordre à variables réelles et sur un cas de bifurcation de cette frontière. Zbl 0171.36602
Mira, C.
4
1966
Extension des notions de points singuliers aux équations aux différences. Zbl 0116.29101
Mira, C.
1
1963
all top 5

Cited by 478 Authors

59 Gardini, Laura
27 Mira, Christian
26 Bischi, Gian-Italo
14 Agliari, Anna
14 Fournier-Prunaret, Danièle
13 Tramontana, Fabio
12 Avrutin, Viktor
11 Rocha, J. Leonel
10 Sushko, Iryna
9 Naimzada, Ahmad K.
8 Cathala, Jean-Claude
8 Gu, Enguo
7 Lamantia, Fabio
7 Millerioux, Gilles
7 Schanz, Michael
6 Cerboni Baiardi, Lorenzo
6 Foroni, Ilaria
6 Mammana, Cristiana
6 Merlone, Ugo
6 Michetti, Elisabetta
6 Mosekilde, Erik
6 Narayaninsamy, Tony
6 Simpson, David John Warwick
5 Carcasses, Jean-Pierre
5 Cima, Anna
5 Dieci, Roberto
5 Fanti, Luciano
5 Gori, Luca
5 Kuznetsov, Aleksandr Petrovich
5 Osinga, Hinke Maria
5 Puu, Tönu
5 Sodini, Mauro
4 Bel’skiĭ, Denis V.
4 Commendatore, Pasquale
4 Dobrynskiĭ, Vladimir A.
4 Gallegati, Mauro
4 Gonchenko, Sergey V.
4 Holmes, Philip J.
4 Kopel, Michael
4 Kubin, Ingrid
4 López-Ruiz, Ricardo
4 Mañosa, Víctor
4 Tikjha, Wirot
4 Zhusubaliev, Zhanybaĭ Tursunbaevich
3 Banerjee, Soumitro
3 Bendoukha, Samir
3 Brianzoni, Serena
3 Daafouz, Jamal
3 Djellit, Ilhem
3 Garijo, Antonio
3 Gasull, Armengol
3 Grácio, Clara
3 Guo, Bao-Zhu
3 Jarque, Xavier
3 Jing, Zhujun
3 Kawakami, Hiroshi
3 Kevrekidis, Ioannis George
3 Krauskopf, Bernd
3 Maistrenko, Yuri L.
3 Makrooni, Roya
3 Nien, Chia-Hsing
3 Peckham, Bruce B.
3 Pelyukh, Grygor P.
3 Shilnikov, Andrey L.
3 Sushko, Irina M.
3 Szidarovszky, Ferenc P.
3 Tatjer, Joan Carles
3 Westerhoff, Frank H.
2 Abdelmalek, Salem
2 Adomaitis, Raymond A.
2 Aihara, Kazuyuki
2 Awrejcewicz, Jan
2 Baram, Yoram
2 Barugola, Alexandre
2 Bashkirtseva, Irina Adol’fovna
2 Bedford, Eric
2 Bezruchko, Boris Petrovich
2 Bi, Qinsheng
2 Caneco, Acilina
2 Cavalli, Fausto
2 Chen, Lansun
2 Chiarella, Carl
2 Cosnard, Michel Y.
2 Dal Forno, Arianna
2 Dawid, Herbert
2 De, Soma
2 Dutta, Partha Sharathi
2 Elsadany, Abdelalim A.
2 Endler, Antônio
2 Futter, Ben
2 Gallas, Jason Alfredo Carlson
2 Garst, Swier
2 Glass, Leon
2 Glendinning, Paul Alexander
2 Gonchenko, Alexander S.
2 Granados, Albert
2 Grebogi, Celso
2 Hittmeyer, Stefanie
2 Huang, Bo
2 Ishii, Yutaka
...and 378 more Authors
all top 5

Cited in 92 Serials

85 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
55 Chaos, Solitons and Fractals
17 Physica D
16 Chaos
12 Mathematics and Computers in Simulation
12 Journal of Difference Equations and Applications
12 Nonlinear Analysis. Theory, Methods & Applications
10 Journal of Economic Dynamics & Control
10 Nonlinear Dynamics
9 Discrete Dynamics in Nature and Society
9 Communications in Nonlinear Science and Numerical Simulation
8 Applied Mathematics and Computation
7 Physics Letters. A
7 Computational Economics
5 Journal of the Franklin Institute
5 Journal of Mathematical Analysis and Applications
5 Mathematical Biosciences
5 Regular and Chaotic Dynamics
4 Journal of Statistical Physics
4 Journal of Nonlinear Science
4 Discrete and Continuous Dynamical Systems. Series B
4 Decisions in Economics and Finance
3 Journal of Mathematical Biology
3 Discrete and Continuous Dynamical Systems
3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
3 Nonlinear Oscillations
2 International Journal of Systems Science
2 Mathematical Methods in the Applied Sciences
2 Mathematical Notes
2 Physica A
2 Bulletin of Mathematical Biology
2 Automatica
2 Journal of Computational and Applied Mathematics
2 RAIRO. Analyse Numérique
2 Acta Mathematicae Applicatae Sinica. English Series
2 Neural Computation
2 SIAM Review
2 Journal of Mathematical Sciences (New York)
2 Complexity
2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
2 Abstract and Applied Analysis
2 Nonlinear Analysis. Real World Applications
2 SIAM Journal on Applied Dynamical Systems
1 International Journal of Modern Physics B
1 Archive for Rational Mechanics and Analysis
1 Astrophysics and Space Science
1 Communications in Mathematical Physics
1 International Journal of Control
1 Nonlinearity
1 Advances in Mathematics
1 Annales de l’Institut Fourier
1 Journal of Combinatorial Theory. Series B
1 Journal of Mathematical Psychology
1 Journal of Soviet Mathematics
1 Michigan Mathematical Journal
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Results in Mathematics
1 SIAM Journal on Control and Optimization
1 Japan Journal of Applied Mathematics
1 Mathematical and Computer Modelling
1 Dynamics and Stability of Systems
1 Annals of Operations Research
1 Aequationes Mathematicae
1 Applied Mathematical Modelling
1 Automation and Remote Control
1 European Journal of Operational Research
1 Historia Mathematica
1 Journal of Dynamics and Differential Equations
1 Indagationes Mathematicae. New Series
1 New Zealand Journal of Mathematics
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Applied Mathematics. Series B (English Edition)
1 Mathematical Problems in Engineering
1 European Journal of Mechanics. A. Solids
1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
1 Qualitative Theory of Dynamical Systems
1 International Journal of Nonlinear Sciences and Numerical Simulation
1 Differential Equations
1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms
1 Dynamical Systems
1 Kragujevac Journal of Mathematics
1 Journal of Systems Science and Complexity
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Journal of Dynamical Systems and Geometric Theories
1 Journal of Function Spaces and Applications
1 Mediterranean Journal of Mathematics
1 Advances in Difference Equations
1 Applications and Applied Mathematics
1 Izvestiya Instituta Matematiki i Informatiki. Udmurtskiĭ Gosudarstvennyĭ Universitet
1 International Journal of Analysis and Applications
1 Arnold Mathematical Journal
1 Journal of Siberian Federal University. Mathematics & Physics
all top 5

Cited in 38 Fields

312 Dynamical systems and ergodic theory (37-XX)
83 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
60 Ordinary differential equations (34-XX)
58 Difference and functional equations (39-XX)
55 Biology and other natural sciences (92-XX)
25 Mechanics of particles and systems (70-XX)
20 Numerical analysis (65-XX)
20 Systems theory; control (93-XX)
12 Information and communication theory, circuits (94-XX)
11 Real functions (26-XX)
10 Global analysis, analysis on manifolds (58-XX)
7 Operations research, mathematical programming (90-XX)
6 History and biography (01-XX)
6 General topology (54-XX)
5 Operator theory (47-XX)
5 Computer science (68-XX)
4 Partial differential equations (35-XX)
3 Measure and integration (28-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Statistics (62-XX)
3 Fluid mechanics (76-XX)
3 Statistical mechanics, structure of matter (82-XX)
2 General and overarching topics; collections (00-XX)
2 Combinatorics (05-XX)
2 Algebraic geometry (14-XX)
2 Convex and discrete geometry (52-XX)
2 Manifolds and cell complexes (57-XX)
2 Probability theory and stochastic processes (60-XX)
1 Number theory (11-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Group theory and generalizations (20-XX)
1 Functions of a complex variable (30-XX)
1 Special functions (33-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Differential geometry (53-XX)
1 Optics, electromagnetic theory (78-XX)
1 Astronomy and astrophysics (85-XX)
1 Geophysics (86-XX)

Citations by Year