Edit Profile (opens in new tab) Mira, Christian Co-Author Distance Author ID: mira.christian Published as: Mira, Christian; Mira, C.; Mira, Ch. more...less Documents Indexed: 148 Publications since 1963, including 9 Books 5 Contributions as Editor · 1 Further Contribution Reviewing Activity: 120 Reviews Co-Authors: 57 Co-Authors with 100 Joint Publications 1,389 Co-Co-Authors all top 5 Co-Authors 52 single-authored 25 Gardini, Laura 21 Gumowski, Igor 11 Bischi, Gian-Italo 11 Kawakami, Hiroshi 7 Millerioux, Gilles 6 Carcasses, Jean-Pierre 6 Cathala, Jean-Claude 5 Fournier, Danielle 4 Simó, Carles 4 Targonski, György I. 3 Agliari, Anna 3 Barugola, Alexandre 3 Fournier-Prunaret, Danièle 3 Hamouly, Hassan El 3 Roubellat, François 2 Allam, Rezk 2 Babary, Jean-Pierre 2 Bernussou, Jacques 2 Bosch, Miquel 2 Couot, Jacques 2 Foroni, Ilaria 2 Gronau, Detlef 2 Hsu, Liu 2 Khammari, Hédi 2 Llibre, Jaume 2 Netzer, Norbert 2 Qriouet, Mohammed 2 Rauzy, Christine 2 Sousa Ramos, José 2 Tatjer, Joan Carles 2 Touzani-Qriouet, M. 1 Abdel-Baset, Heba 1 Abraham, Ralph Herman 1 Alsina, Claudi 1 Burgat, Christian 1 Djellit, Ilhem 1 Förg-Rob, Wolfgang Johann Josef 1 Frouzakis, Christos Emmanouil 1 Gillot, Christian 1 Ginoux, Jean-Marc 1 Grácio, Clara 1 Kevrekidis, Ioannis George 1 Kitajima, Hiroyuki 1 Lagasse, Jean C. 1 Lampreia, José Paulo 1 Maistrenko, Yuri L. 1 Müllenbach, Sabine 1 Myoupo, Jean-Frédéric 1 Narayaninsamy, Tony 1 Pun, Lucas 1 Reich, Ludwig 1 Riberi, Étienne 1 Rouabhi, S. 1 Sevely, Yves 1 Sharkovs’kyĭ, Oleksandr Mykolaĭovych 1 Shilnikov, Andrey L. 1 Sushko, Irina M. 1 Thibault, Roger all top 5 Serials 39 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 29 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 14 Comptes Rendus de l’Académie des Sciences. Série I 6 Grazer Mathematische Berichte 5 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 2 Journal of the Franklin Institute 2 RAIRO, Automatique, Systems Analysis and Control 2 Zagadnienia Drgań Nieliniowych 2 Annales Mathematicae Silesianae 2 Nonlinear Analysis. Theory, Methods & Applications 1 International Journal of Non-Linear Mechanics 1 Chaos, Solitons and Fractals 1 Automatica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications 1 Bulletin de la Classe des Sciences. 5e Série 1 European Journal of Operational Research 1 Regular and Chaotic Dynamics 1 Lecture Notes in Mathematics 1 World Scientific Series on Nonlinear Science. Series A 1 Annales Academiae Paedagogicae Cracoviensis. Studia Mathematica all top 5 Fields 91 Dynamical systems and ergodic theory (37-XX) 28 Ordinary differential equations (34-XX) 21 Difference and functional equations (39-XX) 21 Numerical analysis (65-XX) 13 Global analysis, analysis on manifolds (58-XX) 13 Systems theory; control (93-XX) 12 Mechanics of particles and systems (70-XX) 9 Real functions (26-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 5 Measure and integration (28-XX) 5 Manifolds and cell complexes (57-XX) 5 Biology and other natural sciences (92-XX) 4 Operator theory (47-XX) 4 Information and communication theory, circuits (94-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 General topology (54-XX) 2 Sequences, series, summability (40-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 100 Publications have been cited 921 times in 445 Documents Cited by ▼ Year ▼ Chaotic dynamics in two-dimensional noninvertible maps. Zbl 0906.58027 Mira, Christian; Gardini, Laura; Barugola, Alexandra; Cathala, Jean-Claude 162 1996 Chaotic dynamics. From the one-dimensional endomorphism to the two- dimensional diffeomorphism. Zbl 0641.58002 Mira, Christian 66 1987 Recurrences and discrete dynamic systems. Zbl 0449.58003 Gumowski, Igor; Mira, Christian 51 1980 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. 46 1994 Dynamique chaotique. Transformations ponctuelles. Transition. Ordre - desordre. Zbl 0442.93001 Gumowski, I.; Mira, C. 44 1980 Plane maps with denominator. I: Some generic properties. Zbl 0996.37052 Bischi, Gian-Italo; Gardini, Laura; Mira, Christian 41 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 32 1997 Plane maps with denominator. II: Noninvertible maps with simple focal points. Zbl 1057.37042 Bischi, Gian-Italo; Gardini, Laura; Mira, Christian 20 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. 19 1991 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 18 1997 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 Plane maps with denominator . Part III: Nonsimple focal points and related bifurcations. Zbl 1082.37042 Bischi, Gian-Italo; Gardini, Laura; Mira, Christian 16 2005 On the “crossroad area-saddle area” and “crossroad area-spring area” transitions. Zbl 0874.58060 Mira, C.; Carcassès, J. P. 13 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 “Crossroad area – spring area” transition. II: Foliated parametric representation. Zbl 0876.58035 Mira, C.; Carcassès, J. P.; Bosch, M.; Simó, C.; Tatjer, J. C. 10 1991 Sur la structure des bifurcations des difféomorphismes du cercle. Zbl 0396.58018 Mira, Christian 10 1978 Embedding of a Dim1 piecewise continuous and linear Leonov map into a Dim2 invertible map. Zbl 1296.37033 Mira, Christian 10 2013 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 9 1981 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 Sur l’itération fractionnaire d’un endomorphisme quadratique. Zbl 0546.58012 Mira, Christian; Müllenbach, Sabine 8 1983 Coding scheme based on chaos synchronization from noninvertible maps. Zbl 1002.94029 Millerioux, G.; Mira, C. 8 1998 Sensitivity problems related to certain bifurcations in non-linear recurrence relations. Zbl 0185.18203 Gumowski, I.; Mira, C. 8 1969 Unbounded sets of attraction. Zbl 1090.37511 Bischi, Gian-Italo; Mira, Christian; Gardini, Laura 8 2000 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 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 Bifurcation destabilisant une solution chaotique d’un endomorphisme du deuxième ordre. Zbl 0369.93032 Gumowski, Igor; Mira, Christian 8 1978 Finite-time global chaos synchronization for piecewise linear maps. Zbl 1011.37059 Millerioux, Gilles; Mira, Christian 8 2001 Extensions of the notion of chaotic area in second-order endomorphisms. Zbl 0885.58044 Barugola, A.; Cathala, J. C.; Mira, C. 7 1995 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 On a “crossroad area-spring area” transition occuring in a Duffing-Rayleigh equation with a periodical excitation. Zbl 0896.34029 Mira, Christian; Qriouet, Mohammed 7 1993 Invariant curves and focal points in a Lyness iterative process. Zbl 1063.39016 Gardini, L.; Bischi, G. I.; Mira, C. 7 2003 “Crossroad area – dissymmetrical spring area – symmetrical spring area”, and “double crossroad area – double spring area” transitions. Zbl 0870.58075 Allam, Rezk; Mira, Christian 7 1993 Plane foliation of two-dimensional noninvertible maps. Zbl 0879.58063 Mira, Christian; Carcasses, Jean-Pierre; Millérioux, Gilles; Gardini, Laura 7 1996 Fractal aggregation of basin islands in two-dimensional quadratic noninvertible maps. Zbl 0886.58070 Mira, C.; Rauzy, C. 6 1995 Bifurcation structures generated by the nonautonomous Duffing equation. Zbl 0970.34031 Mira, C.; Touzani-Qriouet, M.; Kawakami, H. 6 1999 Maps with a vanishing denominator. A survey of some results. Zbl 1042.37515 Bischi, Gian-Italo; Gardini, Laura; Mira, Christian 6 2001 Accumulations de bifurcations dans une recurrence. Zbl 0323.26002 Gumowski, Igor; Mira, Christian 6 1975 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 6 2003 Some properties of a two-dimensional piecewise-linear noninvertible map. Zbl 1298.37019 Mira, Christian; Rauzy, Christine; Maistrenko, Yuri; Sushko, Irina 6 1996 Singularites dues au feuilletage du plan des bifurcations d’un difféomorphisme bi-dimensionnel. Zbl 0513.58035 El Hamouly, Hassan; Mira, Christian 5 1982 Some contact bifurcations in two-dimensional examples. Zbl 0930.37038 Fournier-Prunaret, Danièle; Mira, Christian; Gardini, Laura 5 1997 Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0912.34036 Mira, Christian 5 1997 Some historical aspects of nonlinear dynamics: Possible trends for the future. Zbl 0914.34004 Mira, Christian 5 1997 Nonlinear control systems. (Systèmes asservis non linéaires.) Zbl 0864.93008 Mira, Christian 5 1990 Contact bifurcations of absorbing areas and chaotic areas in two-dimensional endomorphisms. Zbl 0919.58050 Gardini, L.; Cathala, J. C.; Mira, C. 5 1996 The dovetail bifurcation structure and its qualitative changes. Zbl 0894.58053 Mira, C.; Kawakami, H.; Allam, R. 5 1993 On the fractal structure of basin boundaries in two-dimensional noninvertible maps. Zbl 1056.37058 Agliari, A.; Gardini, L.; Mira, C. 5 2003 Bifurcation structure in a model of a frequency modulated \(\text{CO}_ 2\) laser. Zbl 0873.34024 Mira, C.; Djellit, I. 5 1993 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 Chaos and fractal properties induced by noninvertibility of models in the form of maps. Zbl 1160.37332 Mira, Christian 4 2000 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 Noninvertible piecewise linear maps applied to chaos synchronization and secure communications. Zbl 0899.58041 Millerioux, G.; Mira, C. 4 1997 Homoclinic and heteroclinic situations specific to two-dimensional noninvertible maps. Zbl 0890.58062 Millerioux, Gilles; Mira, Christian 4 1997 Properties of invariant areas in two-dimensional endomorphisms. Zbl 0917.58040 Gardini, Laura; Mira, Christian; Fournier-Prunaret, Daniele 4 1996 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 Stochastic solutions in a conservative dynamic system. Zbl 0281.34020 Gumowski, I.; Mira, C. 4 1973 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 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 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 Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0886.58050 Mira, Christian 3 1997 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 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 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 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 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 Singularites non classiques d’une recurrence, et d’une équation différentielle d’ordre 2. Zbl 0483.34022 Mira, Christian 1 1981 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 Two applications of noninvertible maps in communication and information storage. Zbl 1001.90009 Mira, C.; Millérioux, G.; Rouabhi, S. 1 2002 Sur quelques problèmes de dynamique complexe. Zbl 0468.58013 Mira, Ch. 1 1981 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 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 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 Rotation sequences and bifurcations structure of one-dimensional endomorphisms. Zbl 0611.58032 Mira, Christian 1 1985 Sur les courbes invariantes fermées des recurrences non linéaires voisines d’une recurrence linéaire conservative du \(2^e\) ordre. Zbl 0368.65060 Mira, C. 1 1976 Sur la double interpretation, déterministe et statistique, de certaines bifurcations complexes. Zbl 0377.65063 Mira, Christian 1 1976 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 History of the theory of nonlinear oscillations. From Poincaré to Andronov. With a preface by Christian Mira. (Histoire de la théorie des oscillations non linéaires. De Poincaré à Andronov.) Zbl 1320.34003 Ginoux, Jean-Marc 1 2015 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 History of the theory of nonlinear oscillations. From Poincaré to Andronov. With a preface by Christian Mira. (Histoire de la théorie des oscillations non linéaires. De Poincaré à Andronov.) Zbl 1320.34003 Ginoux, Jean-Marc 1 2015 Embedding of a Dim1 piecewise continuous and linear Leonov map into a Dim2 invertible map. Zbl 1296.37033 Mira, Christian 10 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 16 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 20 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 embedding of a \((p-1)\)-dimensional noninvertible map into a \(p\)-dimensional invertible map \((p=2,3)\). Zbl 1056.37021 Mira, Christian; Gracio, Clara 6 2003 On the fractal structure of basin boundaries in two-dimensional noninvertible maps. Zbl 1056.37058 Agliari, A.; Gardini, L.; Mira, C. 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 41 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. 8 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 32 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 18 1997 Some contact bifurcations in two-dimensional examples. Zbl 0930.37038 Fournier-Prunaret, Danièle; Mira, Christian; Gardini, Laura 5 1997 Chua’s circuit and the qualitative theory of dynamical systems. Zbl 0912.34036 Mira, Christian 5 1997 Some historical aspects of nonlinear dynamics: Possible trends for the future. Zbl 0914.34004 Mira, Christian 5 1997 Noninvertible piecewise linear maps applied to chaos synchronization and secure communications. Zbl 0899.58041 Millerioux, G.; Mira, C. 4 1997 Homoclinic and heteroclinic situations specific to two-dimensional noninvertible maps. Zbl 0890.58062 Millerioux, Gilles; Mira, Christian 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 162 1996 Plane foliation of two-dimensional noninvertible maps. Zbl 0879.58063 Mira, Christian; Carcasses, Jean-Pierre; Millérioux, Gilles; Gardini, Laura 7 1996 Some properties of a two-dimensional piecewise-linear noninvertible map. Zbl 1298.37019 Mira, Christian; Rauzy, Christine; Maistrenko, Yuri; Sushko, Irina 6 1996 Contact bifurcations of absorbing areas and chaotic areas in two-dimensional endomorphisms. Zbl 0919.58050 Gardini, L.; Cathala, J. C.; Mira, C. 5 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. 46 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 On a “crossroad area-spring area” transition occuring in a Duffing-Rayleigh equation with a periodical excitation. Zbl 0896.34029 Mira, Christian; Qriouet, Mohammed 7 1993 “Crossroad area – dissymmetrical spring area – symmetrical spring area”, and “double crossroad area – double spring area” transitions. Zbl 0870.58075 Allam, Rezk; Mira, Christian 7 1993 The dovetail bifurcation structure and its qualitative changes. Zbl 0894.58053 Mira, C.; Kawakami, H.; Allam, R. 5 1993 Bifurcation structure in a model of a frequency modulated \(\text{CO}_ 2\) laser. Zbl 0873.34024 Mira, C.; Djellit, I. 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. 19 1991 On the “crossroad area-saddle area” and “crossroad area-spring area” transitions. Zbl 0874.58060 Mira, C.; Carcassès, J. P. 13 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. 10 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 5 1990 Chaotic dynamics. From the one-dimensional endomorphism to the two- dimensional diffeomorphism. Zbl 0641.58002 Mira, Christian 66 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 8 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 9 1981 Singularites non classiques d’une recurrence, et d’une équation différentielle d’ordre 2. Zbl 0483.34022 Mira, Christian 1 1981 Sur quelques problèmes de dynamique complexe. Zbl 0468.58013 Mira, Ch. 1 1981 Recurrences and discrete dynamic systems. Zbl 0449.58003 Gumowski, Igor; Mira, Christian 51 1980 Dynamique chaotique. Transformations ponctuelles. Transition. Ordre - desordre. Zbl 0442.93001 Gumowski, I.; Mira, C. 44 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 10 1978 Bifurcation destabilisant une solution chaotique d’un endomorphisme du deuxième ordre. Zbl 0369.93032 Gumowski, Igor; Mira, Christian 8 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 les courbes invariantes fermées des recurrences non linéaires voisines d’une recurrence linéaire conservative du \(2^e\) ordre. Zbl 0368.65060 Mira, C. 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 cited Publications top 5 cited Publications all top 5 Cited by 525 Authors 64 Gardini, Laura 28 Bischi, Gian-Italo 27 Mira, Christian 16 Fournier-Prunaret, Danièle 15 Tramontana, Fabio 13 Agliari, Anna 13 Sushko, Iryna 12 Avrutin, Viktor 12 Rocha, J. Leonel 9 Gu, Enguo 9 Naimzada, Ahmad K. 8 Cathala, Jean-Claude 8 Lamantia, Fabio 7 Merlone, Ugo 7 Michetti, Elisabetta 7 Millerioux, Gilles 7 Schanz, Michael 7 Simpson, David John Warwick 6 Cerboni Baiardi, Lorenzo 6 Foroni, Ilaria 6 Mammana, Cristiana 6 Mosekilde, Erik 6 Narayaninsamy, Tony 6 Tikjha, Wirot 5 Bel’skiĭ, Denis V. 5 Carcasses, Jean-Pierre 5 Cima, Anna 5 Commendatore, Pasquale 5 Dieci, Roberto 5 Fanti, Luciano 5 Gori, Luca 5 Kubin, Ingrid 5 Kuznetsov, Aleksandr Petrovich 5 Mañosa, Víctor 5 Osinga, Hinke Maria 5 Puu, Tönu 5 Sodini, Mauro 4 Djellit, Ilhem 4 Dobrynskiĭ, Vladimir A. 4 Gallegati, Mauro 4 Gonchenko, Sergey V. 4 Grácio, Clara 4 Holmes, Philip J. 4 Kopel, Michael 4 López-Ruiz, Ricardo 4 Pelyukh, Grygor P. 4 Radi, Davide 4 Westerhoff, Frank H. 4 Zhusubaliev, Zhanybaĭ Tursunbaevich 3 Banerjee, Soumitro 3 Bendoukha, Samir 3 Brianzoni, Serena 3 Daafouz, Jamal 3 Garijo, Antonio 3 Gasull, Armengol 3 Grebogi, Celso 3 Guo, Bao-Zhu 3 Jarque, Xavier 3 Jing, Zhujun 3 Kawakami, Hiroshi 3 Kazakov, Alexey O. 3 Kevrekidis, Ioannis George 3 Kitajima, Hiroyuki 3 Krauskopf, Bernd 3 Lozi, René 3 Maistrenko, Yuri L. 3 Makrooni, Roya 3 Nien, Chia-Hsing 3 Panchuk, Anastasiia 3 Peckham, Bruce B. 3 Selmani, Wissame 3 Shilnikov, Andrey L. 3 Sushko, Irina M. 3 Szidarovszky, Ferenc P. 3 Tatjer, Joan Carles 3 Yorke, James Alan 3 Yoshinaga, Tetsuya 2 Abdelmalek, Salem 2 Adomaitis, Raymond A. 2 Aihara, Kazuyuki 2 Amigó, José María 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 Efremova, Lyudmila S. 2 Elaydi, Saber Nasr 2 Elsadany, Abdelalim A. ...and 425 more Authors all top 5 Cited in 96 Serials 88 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 59 Chaos, Solitons and Fractals 18 Physica D 17 Journal of Difference Equations and Applications 16 Chaos 13 Communications in Nonlinear Science and Numerical Simulation 12 Mathematics and Computers in Simulation 12 Nonlinear Dynamics 12 Nonlinear Analysis. 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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 Boletim da Sociedade Paranaense de Matemática. Terceira Série 1 Mediterranean Journal of Mathematics 1 Advances in Difference Equations 1 Applications and Applied Mathematics 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Izvestiya Instituta Matematiki i Informatiki. 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