Edit Profile (opens in new tab) Bonatti, Christian Compute Distance To: Compute Author ID: bonatti.christian Published as: Bonatti, Christian; Bonatti, C.; Bonatti, Ch. more...less Homepage: http://bonatti.perso.math.cnrs.fr/ External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef · theses.fr Documents Indexed: 136 Publications since 1985, including 3 Books 1 Contribution as Editor Co-Authors: 91 Co-Authors with 126 Joint Publications 1,211 Co-Co-Authors all top 5 Co-Authors 11 single-authored 25 Díaz, Lorenzo Justiniano 16 Crovisier, Sylvain 15 Grines, Vyacheslav Zigmundovich 9 Viana, Marcelo 8 Pochinka, Olga Vital’evna 8 Wilkinson, Amie 6 Gómez-Mont, Xavier 6 Potrie, Rafael 5 Abdenur, Flavio 5 Bochi, Jairo 5 Medvedev, Vladislav Sergeevich 5 Pécou, Elisabeth 4 Béguin, François 4 Langevin, Rémi 4 Yang, Dawei 4 Zhang, Jinhua 3 Gan, Shaobo 3 Gogolev, Andrey 3 Gourmelon, Nicolas 3 Guelman, Nancy 3 Shinohara, Katsutoshi 2 Da Luz, Adriana 2 Haefliger, André 2 Hattab, Hawete 2 Kolev, Boris 2 Li, Ming 2 Minkov, Stanislav S. 2 Pujals, Enrique Ramiro 2 Pumariño, Antonio 2 Salhi, Ezzeddine 2 Santiago, Bruno 2 Triestino, Michele 2 Vago, Gioia Maria 2 Wen, Lan 1 Alanís-López, Lilia 1 Alvarez, Sébastien 1 Alves, José Ferreira 1 Arnaud, Marie-Claude 1 Artal Bartolo, Enrique 1 Baladi, Viviane 1 Baraviera, Alexandre Tavares 1 Barthelmé, Thomas 1 Bohnet, Doris 1 Bowden, Jonathan Peter 1 Dolecki, Szymon 1 Dufraine, Emmanuel 1 Eskin, Alex 1 Eynard-Bontemps, Hélène 1 Farinelli, Églantine 1 Firmo, Sebastião 1 Fisher, Todd L. 1 Franks, John M. 1 Gambaudo, Jean-Marc 1 Gelfert, Katrin Grit 1 Gorodetskii, Anton Semenovich 1 Hammerlindl, Andy 1 Jeandenans, E. 1 Kim, Sang-Hyun 1 Kiriki, Shin 1 Koberda, Thomas 1 Kwietniak, Dominik 1 Laudenbach, François 1 Lion, Jean-Marie 1 Lodha, Yash 1 Martínez, Matilde 1 Matheus, Carlos 1 Monteverde, Ignacio 1 Moussu, Robert 1 Navas, Andrés 1 Nogura, Tsugunori 1 Okunev, A. V. 1 Okunev, Alexey 1 Paoluzzi, Luisa 1 Paris, Luis 1 Parwani, Kamlesh 1 Pinsky, Tali 1 Portilla Cuadrado, Pablo 1 Rivas, Cristóbal 1 Rocha, Jorge 1 Rodriguez-Hertz, Federico 1 Schmitt, Bernard 1 Shilin, I. S. 1 Shilin, Ivan 1 Teixeira, Marco Antonio 1 Tresser, Charles 1 Turcat, Gaël 1 Ures, Raúl 1 Vietez, J. L. 1 Villa, Manuel González 1 Villadelprat, Jordi 1 Vivier, Thérèse 1 Vuillemin, F. all top 5 Serials 22 Ergodic Theory and Dynamical Systems 7 Topology 5 Topology and its Applications 4 Israel Journal of Mathematics 4 Nonlinearity 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Proceedings of the London Mathematical Society. Third Series 4 Transactions of the American Mathematical Society 4 Journal of the Institute of Mathematics of Jussieu 3 Commentarii Mathematici Helvetici 3 Fundamenta Mathematicae 3 Publications Mathématiques 3 Inventiones Mathematicae 3 Mathematische Zeitschrift 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Discrete and Continuous Dynamical Systems 3 Geometry & Topology 3 Annals of Mathematics. Second Series 3 Journal of Modern Dynamics 2 Journal of Differential Equations 2 Proceedings of the American Mathematical Society 2 Boletim da Sociedade Brasileira de Matemática. Nova Série 2 Doklady Mathematics 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Proceedings of the Steklov Institute of Mathematics 1 Communications in Mathematical Physics 1 Annales de l’Institut Fourier 1 Duke Mathematical Journal 1 Functional Analysis and its Applications 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Notices of the American Mathematical Society 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Dynamical and Control Systems 1 Algebraic & Geometric Topology 1 Moscow Mathematical Journal 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Astérisque 1 Encyclopaedia of Mathematical Sciences 1 Ensaios Matemáticos 1 Groups, Geometry, and Dynamics 1 Electronic Research Announcements in Mathematical Sciences 1 Science China. Mathematics all top 5 Fields 120 Dynamical systems and ergodic theory (37-XX) 38 Manifolds and cell complexes (57-XX) 5 Several complex variables and analytic spaces (32-XX) 4 General topology (54-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Algebraic topology (55-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 2 Measure and integration (28-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 \(K\)-theory (19-XX) 1 Abstract harmonic analysis (43-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 124 Publications have been cited 2,130 times in 985 Documents Cited by ▼ Year ▼ Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective. Zbl 1060.37020Bonatti, Christian; Díaz, Lorenzo J.; Viana, Marcelo 228 2005 SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Zbl 0962.37012Alves, José F.; Bonatti, Christian; Viana, Marcelo 151 2000 Recurrence and genericity. (Récurrence et généricité.) Zbl 1071.37015Bonatti, Christian; Crovisier, Sylvain 123 2004 SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Zbl 0996.37033Bonatti, Christian; Viana, Marcelo 121 2000 A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources. Zbl 1049.37011Bonatti, C.; Díaz, L. J.; Pujals, E. R. 120 2003 Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms. Zbl 1246.37040Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 77 2011 Persistent nonhyperbolic transitive diffeomorphisms. Zbl 0852.58066Bonatti, Christian; Díaz, Lorenzo J. 75 1996 Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). Zbl 0959.37017Bonatti, C.; Grines, V. 46 2000 Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices). Zbl 1025.37018Bonatti, Christian; Gómez-Mont, Xavier; Viana, Marcelo 43 2003 Robust heterodimensional cycles and \(C^1\)-generic dynamics. Zbl 1156.37004Bonatti, Christian; Díaz, Lorenzo J. 42 2008 Perturbations of the derivative along periodic orbits. Zbl 1175.37027Bonatti, Christian; Gourmelon, Nikolas; Vivier, Thérèse 39 2006 Transitive partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1074.57015Bonatti, Christian; Wilkinson, Amie 35 2005 Periodic points and homoclinic classes. Zbl 1144.37007Abdenur, F.; Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wen, L. 34 2007 Removing zero Lyapunov exponents. Zbl 1048.37026Baraviera, Alexandre T.; Bonatti, Christian 34 2003 Lyapunov exponents with multiplicity 1 for deterministic products of matrices. Zbl 1087.37017Bonatti, C.; Viana, M. 31 2004 Lorenz attractors with arbitrary expanding dimension. Zbl 0896.58043Bonatti, Christian; Pumariño, António; Viana, Marcelo 27 1997 Robust criterion for the existence of nonhyperbolic ergodic measures. Zbl 1368.37036Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. 25 2016 Abundance of \(C^{1}\)-robust homoclinic tangencies. Zbl 1300.37013Bonatti, Christian; Díaz, Lorenzo J. 25 2012 Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms. Zbl 1031.37030Bonatti, Christian; Díaz, Lorenzo J.; Ures, Raúl 24 2002 There is no “Shadowing lemma” for partially hyperbolic dynamics. (Pas de “Shadowing Lemma” pour les dynamiques partiellement hyperboliques.) Zbl 0973.37016Bonatti, Christian; Díaz, Lorenzo J.; Turcat, Gaël 23 2000 On maximal transitive sets of generic diffeomorphisms. Zbl 1032.37011Bonatti, Christian; Dıaz, Lorenzo J. 23 2002 Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Zbl 1157.37309Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 22 2002 Topological classification of gradient-like diffeomorphisms on 3-manifolds. Zbl 1056.37023Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 22 2004 The \(C^1\) generic diffeomorphism has trivial centralizer. Zbl 1177.37025Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 21 2009 Robustly transitive sets and heterodimensional cycles. Zbl 1056.37024Bonatti, Christian; Díaz, Lorenzo J.; Pujals, Enrique R.; Rocha, Jorge 21 2003 Towards a global view of dynamical systems, for the \(C^{1}\)-topology. Zbl 1256.37006Bonatti, C. 21 2011 Classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic orbits on 3-manifolds. Zbl 1138.37307Bonatti, C.; Grines, V. Z.; Pochinka, O. V. 18 2005 Non-hyperbolic ergodic measures with large support. Zbl 1195.37013Bonatti, Christian; Díaz, Lorenzo J.; Gorodetski, Anton 18 2010 Stabilization of heterodimensional cycles. Zbl 1284.37020Bonatti, C.; Díaz, L. J.; Kiriki, S. 17 2012 Heteroclinic connections and genericity of infinitely many sinks and sources. (Connexions hétéroclines et généricité d’une infinité de puits et de sources.) Zbl 0944.37012Bonatti, Christian; Díaz, Lorenzo 17 1999 Smale diffeomorphisms of surfaces. With the collab. of Emmanuelle Jeandenans. (Difféomorphismes de Smale des surfaces. Avec la collaboration d’Emmanuelle Jeandenans.) Zbl 0922.58058Bonatti, C.; Langevin, R. 17 1998 Un point fixe commun pour des difféomorphismes commutants de \(S^ 2\). (A common fixed point for commutating diffeomorphisms of \(S^ 2\).). Zbl 0689.57019Bonatti, Christian 17 1989 An example of transitive Anosov flows transversal to a torus and not conjugated to a suspension. (Un exemple de flot d’Anosov transitif transverse à un tore et non conjugué à une suspension.) Zbl 0826.58026Bonatti, Christian; Langevin, Remi 16 1994 Non-wandering sets with non-empty interiors. Zbl 1083.37020Abdenur, Flavio; Bonatti, Christian; Díaz, Lorenzo J. 16 2004 Perturbation of the Lyapunov spectra of periodic orbits. Zbl 1268.37027Bochi, J.; Bonatti, C. 15 2012 Statistical behaviour of the leaves of certain holomorphic foliations. (Sur le comportement statistique des feuilles de certains feuilletages holomorphes.) Zbl 1010.37025Bonatti, Christian; Gómez-Mont, Xavier 15 2001 Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples. Zbl 1370.37069Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael 15 2016 Generic symplectic dynamics. (Dynamiques symplectiques génériques.) Zbl 1084.37017Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain 14 2005 Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics. Zbl 1362.37075Bohnet, Doris; Bonatti, Christian 14 2016 On the existence of non-trivial homoclinic classes. Zbl 1128.37021Bonatti, Christian; Gan, Shaobo; Wen, Lan 13 2007 Local density of diffeomorphisms with large centralizers. Zbl 1163.58003Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie 13 2008 Abnormal escape rates from nonuniformly hyperbolic sets. Zbl 0987.37018Baladi, Viviane; Bonatti, Christian; Schmitt, Bernard 12 1999 The \(C^{1+\alpha}\) hypothesis in Pesin theory revisited. Zbl 1312.37018Bonatti, Christian; Crovisier, Sylvain; Shinohara, Katsutoshi 12 2013 Generic diffeomorphisms on compact surfaces. Zbl 1089.37032Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain; Díaz, Lorenzo J. 12 2005 On the hyperbolicity of homoclinic classes. Zbl 1200.37023Bonatti, Christian; Gan, Shaobo; Yang, Dawei 11 2009 Rigidity for \(C^1\) actions on the interval arising from hyperbolicity. I: Solvable groups. Zbl 1433.37030Bonatti, C.; Monteverde, Ignacio; Navas, Andres; Rivas, Cristobal 11 2017 Difféomorphismes commutants des surfaces et stabilité des fibrations en tores. (Commuting diffeomorphisms of surfaces and stability of fibrations by tori). Zbl 0703.57015Bonatti, Christian 11 1990 Foliations in \(\mathbb{C} P(n)\): About hyperbolic holonomy for minimal exceptional sets. (Feuilletages de \(\mathbf C\mathbf P(n)\): De l’holonomie hyperbolique pour les minimaux exceptionnels.) Zbl 0782.32023Bonatti, C.; Langevin, R.; Moussu, R. 10 1992 Robust vanishing of all Lyapunov exponents for iterated function systems. Zbl 1284.37044Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. 10 2014 Smale flows in dimension 3: finite presentations of invariant neighbourhoods of saddle sets. (Flots de Smale en dimension 3: Présentations finies de voisinages invariants d’ensembles selles.) Zbl 1102.37307Béguin, F.; Bonatti, C. 10 2002 Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication. Zbl 1303.37008Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Gourmelon, N. 10 2013 Statistical behaviour of the leaves of Riccati foliations. Zbl 1209.37055Bonatti, Ch.; Gómez-Mont, X.; Vila-Freyer, R. 10 2010 Axiom A diffeomorphisms derived from Anosov flows. Zbl 1201.37033Bonatti, Christian; Guelman, Nancy 10 2010 Anomalous partially hyperbolic diffeomorphisms. I: Dynamically coherent examples. (Difféomorphismes partiellement hyperboliques anormaux. I: Exemples dynamiquement cohérents.) Zbl 1375.37093Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael 10 2016 Center manifolds for partially hyperbolic sets without strong unstable connections. Zbl 1362.37069Bonatti, Christian; Crovisier, Sylvain 9 2016 Building Anosov flows on 3-manifolds. Zbl 1375.37083Béguin, François; Bonatti, Christian; Yu, Bin 9 2017 Dominated Pesin theory: convex sum of hyperbolic measures. Zbl 1408.37054Bochi, Jairo; Bonatti, Christian; Gelfert, Katrin 9 2018 Roots in the mapping class groups. Zbl 1160.57014Bonatti, Christian; Paris, Luis 9 2009 What is \(\ldots a\) blender? Zbl 1352.37075Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wilkinson, A. 9 2016 \(C^1\)-generic conservative diffeomorphisms have trivial centralizer. Zbl 1149.37017Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 8 2008 Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Zbl 1153.37340Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pochinka, O. V. 8 2007 Commuting analytic vector fields in dimension 3 or 4: Existence of common zeros. (Champs de vecteurs analytiques commutants, en dimension 3 ou 4: Existence de zeros communs.) Zbl 0776.57013Bonatti, Christian 8 1992 Dominated chain recurrent class with singularities. Zbl 1371.37027Bonatti, Christian; Gan, Shaobo; Yang, Dawei 8 2015 Periodic measures and partially hyperbolic homoclinic classes. Zbl 1421.37018Bonatti, Christian; Zhang, Jinhua 7 2019 Super exponential growth of the number of periodic orbits inside homoclinic classes. Zbl 1145.37015Bonatti, Christian; Díaz, Lorenzo J.; Fisher, Todd 7 2008 Discontinuity of the Hausdorff dimension of hyperbolic sets. Zbl 0852.54038Bonatti, Christian; Díaz, Lorenzo Justiniano; Viana, Marcelo 7 1995 Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds. Zbl 1435.37050Bonatti, C.; Grines, V.; Pochinka, O. 7 2019 Abundance of stable ergodicity. Zbl 1052.37023Bonatti, Christian; Matheus, Carlos; Viana, Marcelo; Wilkinson, Amie 7 2004 Global dominated splittings and the \( C^1\) Newhouse phenomenon. Zbl 1088.37013Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 7 2006 On the topological classification of gradient-like diffeomorphisms without heteroclinic curves on three-dimensional manifolds. Zbl 1041.37007Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pecou, E. 7 2001 Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds. Zbl 1222.37021Bonatti, Christian; Grines, Viacheslav; Pochinka, Olga 7 2006 Anomalous partially hyperbolic diffeomorphisms. III: Abundance and incoherence. Zbl 1470.37049Bonatti, Christian; Gogolev, Andrey; Hammerlindl, Andy; Potrie, Rafael 6 2020 3-manifolds which are orbit spaces of diffeomorphisms. Zbl 1165.37001Bonatti, C.; Paoluzzi, L. 6 2008 Compact leaves of a generic codimension 1 foliation. (Feuilles compactes d’un feuilletage générique en codimension 1.) Zbl 0828.57022Bonatti, Christian; Firmo, Sebastião 6 1994 Two-dimensional links and diffeomorphisms on 3-manifolds. Zbl 1008.37013Bonatti, Christian; Grines, Viatcheslav; Pécou, Elisabeth 6 2002 On Morse-Smale diffeomorphisms without heteroclinic intersections on three-manifolds. Zbl 1011.37013Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pécou, E. 6 2002 A robustly chain transitive attractor with singularities of different indices. Zbl 1304.37002Bonatti, Christian; Li, Ming; Yang, Dawei 6 2013 Déformations de feuilletages. (Deformations of foliations). Zbl 0703.57013Bonatti, C.; Haefliger, A. 6 1990 Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center. Zbl 1472.37034Bonatti, Christian; Zhang, Jinhua 5 2020 A criterion for zero averages and full support of ergodic measures. Zbl 07069469Bonatti, Christian; Díaz, Lorenzo J.; Bochi, Jairo 5 2018 Foliations near to a fibration. (Feuilletages proches d’une fibration.) Zbl 1214.53022Bonatti, C. 5 1993 On the existence of attractors. Zbl 1272.37019Bonatti, Christian; Li, Ming; Yang, Dawei 5 2013 Quasi-orbit spaces associated to \(T_0\)-spaces. Zbl 1218.54025Bonatti, C.; Hattab, H.; Salhi, E. 5 2011 The index of holomorphic vector fields on singular varieties. I. Zbl 0810.32017Bonatti, Ch.; Gómez-Mont, X. 5 1994 Wandering domains for infinitely renormalizable diffeomorphisms of the disk. Zbl 0843.57016Bonatti, Christian; Gambaudo, Jean Marc; Lion, Jean Marie; Tresser, Charles 5 1994 Topological equivalence of saddle connections in dimension 3. (Équivalence topologique de connexions de selles en dimension 3.) Zbl 1056.37030Bonatti, Christian; Dufraine, Emmanuel 5 2003 Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds. Zbl 1431.37032Bonatti, Ch.; Grines, V.; Laudenbach, F.; Pochinka, O. 4 2019 Transitive Anosov flows and Axiom-A diffeomorphisms. Zbl 1173.37028Bonatti, Christian; Guelman, Nancy 4 2009 Dynamical systems in dimension 2 and 3: conjugacy invariants and classification. Zbl 1121.37306Bonatti, C.; Grines, V.; Langevin, R. 4 2001 Centralizers of \(C^1\)-contractions of the half line. Zbl 1326.22019Bonatti, Christian; Farinelli, Églantine 4 2015 Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1380.37065Bonatti, Christian; Zhang, Jinhua 4 2017 Realization of Morse-Smale diffeomorphisms on 3-manifolds. Zbl 1377.37044Bonatti, Ch.; Grines, V. Z.; Pochinka, Olga V. 4 2017 Cubic tangencies and hyperbolic diffeomorphisms. Zbl 0943.37012Bonatti, Ch.; Díaz, L. J.; Vuillemin, F. 4 1998 Hasse diagrams and orbit class spaces. Zbl 1213.54050Bonatti, C.; Hattab, H.; Salhi, E.; Vago, G. 4 2011 The index of stable critical points. Zbl 1013.37016Bonatti, Christian; Villadelprat, Jordi 4 2002 Star flows and multisingular hyperbolicity. Zbl 1487.37037Bonatti, Christian; Da Luz, Adriana 3 2021 Hyperbolicity as an obstruction to smoothability for one-dimensional actions. Zbl 1428.37029Bonatti, Christian; Lodha, Yash; Triestino, Michele 3 2019 The centralizer of a \(C^1\)-generic diffeomorphism is trivial. Zbl 1149.37012Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 3 2008 A Hölder continuous vector field tangent to many foliations. Zbl 1147.37313Bonatti, Christian; Franks, John 3 2004 Fragile cycles. Zbl 1279.37022Bonatti, Ch.; Díaz, L. J. 3 2012 Star flows and multisingular hyperbolicity. Zbl 1487.37037Bonatti, Christian; Da Luz, Adriana 3 2021 Robust existence of nonhyperbolic ergodic measures with positive entropy and full support. Zbl 1492.37040Bonatti, Christian; Díaz, Lorenzo J.; Kwietniak, Dominik 1 2021 Anomalous Anosov flows revisited. Zbl 1495.37030Barthelmé, Thomas; Bonatti, Christian; Gogolev, Andrey; Rodriguez Hertz, Federico 1 2021 Anomalous partially hyperbolic diffeomorphisms. III: Abundance and incoherence. Zbl 1470.37049Bonatti, Christian; Gogolev, Andrey; Hammerlindl, Andy; Potrie, Rafael 6 2020 Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center. Zbl 1472.37034Bonatti, Christian; Zhang, Jinhua 5 2020 Foliated hyperbolicity and foliations with hyperbolic leaves. Zbl 1439.37041Bonatti, Christian; Gómez-Mont, Xavier; Martínez, Matilde 2 2020 Projective cocycles over \(\operatorname{SL}(2,\mathbb{R})\) actions: measures invariant under the upper triangular group. Zbl 1470.37042Bonatti, Christian; Eskin, Alex; Wilkinson, Amie 1 2020 Periodic measures and partially hyperbolic homoclinic classes. Zbl 1421.37018Bonatti, Christian; Zhang, Jinhua 7 2019 Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds. Zbl 1435.37050Bonatti, C.; Grines, V.; Pochinka, O. 7 2019 Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds. Zbl 1431.37032Bonatti, Ch.; Grines, V.; Laudenbach, F.; Pochinka, O. 4 2019 Hyperbolicity as an obstruction to smoothability for one-dimensional actions. Zbl 1428.37029Bonatti, Christian; Lodha, Yash; Triestino, Michele 3 2019 Dominated Pesin theory: convex sum of hyperbolic measures. Zbl 1408.37054Bochi, Jairo; Bonatti, Christian; Gelfert, Katrin 9 2018 A criterion for zero averages and full support of ergodic measures. Zbl 07069469Bonatti, Christian; Díaz, Lorenzo J.; Bochi, Jairo 5 2018 Many intermingled basins in dimension 3. Zbl 1398.37017Bonatti, Christian; Potrie, Rafael 3 2018 Weak hyperbolic structures and robust properties of diffeomorphisms and flows. Zbl 1401.37037Bonatti, Christian; da Luz, Adriana 2 2018 Volume hyperbolicity and wildness. Zbl 1390.37049Bonatti, Christian; Shinohara, Katsutoshi 1 2018 Rigidity for \(C^1\) actions on the interval arising from hyperbolicity. I: Solvable groups. Zbl 1433.37030Bonatti, C.; Monteverde, Ignacio; Navas, Andres; Rivas, Cristobal 11 2017 Building Anosov flows on 3-manifolds. Zbl 1375.37083Béguin, François; Bonatti, Christian; Yu, Bin 9 2017 Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1380.37065Bonatti, Christian; Zhang, Jinhua 4 2017 Realization of Morse-Smale diffeomorphisms on 3-manifolds. Zbl 1377.37044Bonatti, Ch.; Grines, V. Z.; Pochinka, Olga V. 4 2017 Existence of common zeros for commuting vector fields on three manifolds. (Existence de zéros communs pour les champs de vecteurs qui commutent sur les 3-variétés.) Zbl 1405.37026Bonatti, Christian; Santiago, Bruno 1 2017 A \(C^1\) Anosov diffeomorphism with a horseshoe that attracts almost any point. Zbl 1377.37047Bonatti, C.; Minkov, S. S.; Okunev, A. V.; Shilin, I. S. 1 2017 Robust criterion for the existence of nonhyperbolic ergodic measures. Zbl 1368.37036Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. 25 2016 Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples. Zbl 1370.37069Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael 15 2016 Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics. Zbl 1362.37075Bohnet, Doris; Bonatti, Christian 14 2016 Anomalous partially hyperbolic diffeomorphisms. I: Dynamically coherent examples. (Difféomorphismes partiellement hyperboliques anormaux. I: Exemples dynamiquement cohérents.) Zbl 1375.37093Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael 10 2016 Center manifolds for partially hyperbolic sets without strong unstable connections. Zbl 1362.37069Bonatti, Christian; Crovisier, Sylvain 9 2016 What is \(\ldots a\) blender? Zbl 1352.37075Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wilkinson, A. 9 2016 Connectedness of the space of smooth actions of \(\mathbb{Z}^{n}\) on the interval. Zbl 1375.37081Bonatti, Christian; Eynard-Bontemps, Hélène 2 2016 A spectral-like decomposition for transitive Anosov flows in dimension three. Zbl 1384.37038Beguin, F.; Bonatti, C.; Yu, B. 1 2016 Dominated chain recurrent class with singularities. Zbl 1371.37027Bonatti, Christian; Gan, Shaobo; Yang, Dawei 8 2015 Centralizers of \(C^1\)-contractions of the half line. Zbl 1326.22019Bonatti, Christian; Farinelli, Églantine 4 2015 Flexible periodic points. Zbl 1352.37076Bonatti, Christian; Shinohara, Katsutoshi 2 2015 Robust vanishing of all Lyapunov exponents for iterated function systems. Zbl 1284.37044Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. 10 2014 Smooth conjugacy classes of circle diffeomorphisms with irrational rotation number. Zbl 1346.37045Bonatti, Christian; Guelman, Nancy 2 2014 Tame dynamics and robust transitivity chain-recurrence classes versus homoclinic classes. Zbl 1309.37025Bonatti, C.; Crovisier, S.; Gourmelon, N.; Potrie, R. 1 2014 The \(C^{1+\alpha}\) hypothesis in Pesin theory revisited. Zbl 1312.37018Bonatti, Christian; Crovisier, Sylvain; Shinohara, Katsutoshi 12 2013 Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication. Zbl 1303.37008Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Gourmelon, N. 10 2013 A robustly chain transitive attractor with singularities of different indices. Zbl 1304.37002Bonatti, Christian; Li, Ming; Yang, Dawei 6 2013 On the existence of attractors. Zbl 1272.37019Bonatti, Christian; Li, Ming; Yang, Dawei 5 2013 Abundance of \(C^{1}\)-robust homoclinic tangencies. Zbl 1300.37013Bonatti, Christian; Díaz, Lorenzo J. 25 2012 Stabilization of heterodimensional cycles. Zbl 1284.37020Bonatti, C.; Díaz, L. J.; Kiriki, S. 17 2012 Perturbation of the Lyapunov spectra of periodic orbits. Zbl 1268.37027Bochi, J.; Bonatti, C. 15 2012 Fragile cycles. Zbl 1279.37022Bonatti, Ch.; Díaz, L. J. 3 2012 Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms. Zbl 1246.37040Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 77 2011 Towards a global view of dynamical systems, for the \(C^{1}\)-topology. Zbl 1256.37006Bonatti, C. 21 2011 Quasi-orbit spaces associated to \(T_0\)-spaces. Zbl 1218.54025Bonatti, C.; Hattab, H.; Salhi, E. 5 2011 Hasse diagrams and orbit class spaces. Zbl 1213.54050Bonatti, C.; Hattab, H.; Salhi, E.; Vago, G. 4 2011 Non-hyperbolic ergodic measures with large support. Zbl 1195.37013Bonatti, Christian; Díaz, Lorenzo J.; Gorodetski, Anton 18 2010 Statistical behaviour of the leaves of Riccati foliations. Zbl 1209.37055Bonatti, Ch.; Gómez-Mont, X.; Vila-Freyer, R. 10 2010 Axiom A diffeomorphisms derived from Anosov flows. Zbl 1201.37033Bonatti, Christian; Guelman, Nancy 10 2010 The \(C^1\) generic diffeomorphism has trivial centralizer. Zbl 1177.37025Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 21 2009 On the hyperbolicity of homoclinic classes. Zbl 1200.37023Bonatti, Christian; Gan, Shaobo; Yang, Dawei 11 2009 Roots in the mapping class groups. Zbl 1160.57014Bonatti, Christian; Paris, Luis 9 2009 Transitive Anosov flows and Axiom-A diffeomorphisms. Zbl 1173.37028Bonatti, Christian; Guelman, Nancy 4 2009 Robust heterodimensional cycles and \(C^1\)-generic dynamics. Zbl 1156.37004Bonatti, Christian; Díaz, Lorenzo J. 42 2008 Local density of diffeomorphisms with large centralizers. Zbl 1163.58003Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie 13 2008 \(C^1\)-generic conservative diffeomorphisms have trivial centralizer. Zbl 1149.37017Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 8 2008 Super exponential growth of the number of periodic orbits inside homoclinic classes. Zbl 1145.37015Bonatti, Christian; Díaz, Lorenzo J.; Fisher, Todd 7 2008 3-manifolds which are orbit spaces of diffeomorphisms. Zbl 1165.37001Bonatti, C.; Paoluzzi, L. 6 2008 The centralizer of a \(C^1\)-generic diffeomorphism is trivial. Zbl 1149.37012Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 3 2008 Periodic points and homoclinic classes. Zbl 1144.37007Abdenur, F.; Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wen, L. 34 2007 On the existence of non-trivial homoclinic classes. Zbl 1128.37021Bonatti, Christian; Gan, Shaobo; Wen, Lan 13 2007 Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Zbl 1153.37340Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pochinka, O. V. 8 2007 Perturbations of the derivative along periodic orbits. Zbl 1175.37027Bonatti, Christian; Gourmelon, Nikolas; Vivier, Thérèse 39 2006 Global dominated splittings and the \( C^1\) Newhouse phenomenon. Zbl 1088.37013Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 7 2006 Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds. Zbl 1222.37021Bonatti, Christian; Grines, Viacheslav; Pochinka, Olga 7 2006 Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective. Zbl 1060.37020Bonatti, Christian; Díaz, Lorenzo J.; Viana, Marcelo 228 2005 Transitive partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1074.57015Bonatti, Christian; Wilkinson, Amie 35 2005 Classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic orbits on 3-manifolds. Zbl 1138.37307Bonatti, C.; Grines, V. Z.; Pochinka, O. V. 18 2005 Generic symplectic dynamics. (Dynamiques symplectiques génériques.) Zbl 1084.37017Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain 14 2005 Generic diffeomorphisms on compact surfaces. Zbl 1089.37032Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain; Díaz, Lorenzo J. 12 2005 Recurrence and genericity. (Récurrence et généricité.) Zbl 1071.37015Bonatti, Christian; Crovisier, Sylvain 123 2004 Lyapunov exponents with multiplicity 1 for deterministic products of matrices. Zbl 1087.37017Bonatti, C.; Viana, M. 31 2004 Topological classification of gradient-like diffeomorphisms on 3-manifolds. Zbl 1056.37023Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 22 2004 Non-wandering sets with non-empty interiors. Zbl 1083.37020Abdenur, Flavio; Bonatti, Christian; Díaz, Lorenzo J. 16 2004 Abundance of stable ergodicity. Zbl 1052.37023Bonatti, Christian; Matheus, Carlos; Viana, Marcelo; Wilkinson, Amie 7 2004 A Hölder continuous vector field tangent to many foliations. Zbl 1147.37313Bonatti, Christian; Franks, John 3 2004 Classification of Morse-Smale diffeomorphisms with finite sets of heteroclinic orbits on 3-manifolds. Zbl 1282.37022Bonatti, Ch.; Grines, V. Z.; Pochina, O. V. 1 2004 A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources. Zbl 1049.37011Bonatti, C.; Díaz, L. J.; Pujals, E. R. 120 2003 Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices). Zbl 1025.37018Bonatti, Christian; Gómez-Mont, Xavier; Viana, Marcelo 43 2003 Removing zero Lyapunov exponents. Zbl 1048.37026Baraviera, Alexandre T.; Bonatti, Christian 34 2003 Robustly transitive sets and heterodimensional cycles. Zbl 1056.37024Bonatti, Christian; Díaz, Lorenzo J.; Pujals, Enrique R.; Rocha, Jorge 21 2003 Topological equivalence of saddle connections in dimension 3. (Équivalence topologique de connexions de selles en dimension 3.) Zbl 1056.37030Bonatti, Christian; Dufraine, Emmanuel 5 2003 Recurrence and genericity. Zbl 1027.37011Bonatti, Christian; Crovisier, Sylvain 3 2003 Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms. Zbl 1031.37030Bonatti, Christian; Díaz, Lorenzo J.; Ures, Raúl 24 2002 On maximal transitive sets of generic diffeomorphisms. Zbl 1032.37011Bonatti, Christian; Dıaz, Lorenzo J. 23 2002 Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Zbl 1157.37309Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 22 2002 Smale flows in dimension 3: finite presentations of invariant neighbourhoods of saddle sets. (Flots de Smale en dimension 3: Présentations finies de voisinages invariants d’ensembles selles.) Zbl 1102.37307Béguin, F.; Bonatti, C. 10 2002 Two-dimensional links and diffeomorphisms on 3-manifolds. Zbl 1008.37013Bonatti, Christian; Grines, Viatcheslav; Pécou, Elisabeth 6 2002 On Morse-Smale diffeomorphisms without heteroclinic intersections on three-manifolds. Zbl 1011.37013Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pécou, E. 6 2002 The index of stable critical points. Zbl 1013.37016Bonatti, Christian; Villadelprat, Jordi 4 2002 \(C^1\)-generic dynamics: Tame and wild behaviour. Zbl 1136.37318Bonatti, C. 1 2002 Statistical behaviour of the leaves of certain holomorphic foliations. (Sur le comportement statistique des feuilles de certains feuilletages holomorphes.) Zbl 1010.37025Bonatti, Christian; Gómez-Mont, Xavier 15 2001 On the topological classification of gradient-like diffeomorphisms without heteroclinic curves on three-dimensional manifolds. Zbl 1041.37007Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pecou, E. 7 2001 Dynamical systems in dimension 2 and 3: conjugacy invariants and classification. Zbl 1121.37306Bonatti, C.; Grines, V.; Langevin, R. 4 2001 SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Zbl 0962.37012Alves, José F.; Bonatti, Christian; Viana, Marcelo 151 2000 SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Zbl 0996.37033Bonatti, Christian; Viana, Marcelo 121 2000 Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). Zbl 0959.37017Bonatti, C.; Grines, V. 46 2000 There is no “Shadowing lemma” for partially hyperbolic dynamics. (Pas de “Shadowing Lemma” pour les dynamiques partiellement hyperboliques.) Zbl 0973.37016Bonatti, Christian; Díaz, Lorenzo J.; Turcat, Gaël 23 2000 ...and 24 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 684 Authors 49 Bonatti, Christian 42 Grines, Vyacheslav Zigmundovich 42 Pochinka, Olga Vital’evna 35 Lee, Manseob 26 Varandas, Paulo 22 Alves, José Ferreira 22 Díaz, Lorenzo Justiniano 22 Viana, Marcelo 21 Araújo, Vítor 21 Bessa, Mário 21 Morales, Carlos Arnoldo 21 Yang, Jiagang 20 Crovisier, Sylvain 20 Medvedev, Vladislav Sergeevich 19 Potrie, Rafael 19 Zhuzhoma, Evgeniĭ Viktorovich 18 Gan, Shaobo 18 Gelfert, Katrin Grit 17 Bochi, Jairo 17 Yang, Dawei 14 Hammerlindl, Andy 13 Tahzibi, Ali 12 Barrientos, Pablo G. 11 Avila, Artur 11 Pacifico, Maria José 11 Pinheiro, Vilton 11 Pujals, Enrique Ramiro 11 Shi, Yi 10 Gurevich, Elena Ya. 10 Luzzatto, Stefano 10 Rocha, Jorge 10 Rodriguez Hertz, Jana 10 Tian, Xueting 9 Alvarez, Sébastien 9 Arbieto, Alexander 9 Climenhaga, Vaughn 9 Pesin, Yakov Borisovich 9 Rams, Michał 9 Rodriguez-Hertz, Federico 9 Sumi, Naoya 9 Zhang, Jinhua 9 Zhou, Yunhua 8 Cao, Yongluo 8 Dolgopyat, Dmitry 8 Fisher, Todd L. 8 Gorodetskii, Anton Semenovich 8 Sambarino, Martín 8 Sun, Wenxiang 8 Ures, Raúl 7 Backes, Lucas H. 7 Carrasco, Pablo D. 7 Fakhari, Abbas 7 Hirsch, Morris W. 7 Liang, Chao 7 Nakano, Yushi 7 Santiago, Bruno 7 Shinohara, Katsutoshi 7 Turaev, Dmitry V. 7 Wen, Xiao 7 Zhu, Yujun 6 Asaoka, Masayuki 6 Bautista, Serafín 6 Berger, Pierre 6 Fenley, Sérgio R. 6 Kiriki, Shin 6 Krauskopf, Bernd 6 Liao, Gang 6 Lopes Dias, João 6 Nozdrinova, Elena V. 6 Oliveira, Krerley 6 Osinga, Hinke Maria 6 Pérez, Sebastian A. 6 Saghin, Radu 6 Soma, Teruhiko 6 Vásquez, Carlos H. 6 Wang, Xiaodong 6 Wen, Lan 6 Wilkinson, Amie 5 Andersson, Martin 5 Béguin, François 5 Castro, Armando 5 Catalan, Thiago 5 Catsigeras, Eleonora 5 Da Luz, Adriana 5 Firmo, Sebastião 5 Gogolev, Andrey 5 Gómez-Mont, Xavier 5 Gourmelon, Nicolas 5 Homburg, Ale Jan 5 Kleptsyn, Victor A. 5 Laudenbach, François 5 Lee, Keonhee 5 Lizana, Cristina 5 Mi, Zeya 5 Navas, Andrés 5 Nguyên Viêt Anh 5 Obata, Davi 5 Sakai, Kazuhiro 5 Salgado, Luciana 5 Sibony, Nessim ...and 584 more Authors all top 5 Cited in 160 Serials 119 Ergodic Theory and Dynamical Systems 53 Discrete and Continuous Dynamical Systems 39 Mathematische Zeitschrift 38 Proceedings of the American Mathematical Society 35 Journal of Differential Equations 33 Transactions of the American Mathematical Society 33 Dynamical Systems 27 Communications in Mathematical Physics 23 Israel Journal of Mathematics 23 Advances in Mathematics 23 Annales de l’Institut Henri Poincaré. 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Serie V 2 Journal of Fixed Point Theory and Applications 2 Mathematics Research Reports 2 Russian Journal of Nonlinear Dynamics 1 Journal of Mathematical Physics 1 The Mathematical Intelligencer 1 Acta Mathematica Vietnamica 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Colloquium Mathematicum 1 Dissertationes Mathematicae 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Journal of Geometry 1 Journal of the London Mathematical Society. Second Series ...and 60 more Serials all top 5 Cited in 42 Fields 913 Dynamical systems and ergodic theory (37-XX) 109 Manifolds and cell complexes (57-XX) 40 Ordinary differential equations (34-XX) 37 Measure and integration (28-XX) 36 Several complex variables and analytic spaces (32-XX) 36 Differential geometry (53-XX) 32 General topology (54-XX) 31 Global analysis, analysis on manifolds (58-XX) 20 Probability theory and stochastic processes (60-XX) 17 Group theory and generalizations (20-XX) 12 Functions of a complex variable (30-XX) 11 Mechanics of particles and systems (70-XX) 10 Algebraic topology (55-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Operator theory (47-XX) 7 Algebraic geometry (14-XX) 6 Topological groups, Lie groups (22-XX) 6 Partial differential equations (35-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Difference and functional equations (39-XX) 4 Numerical analysis (65-XX) 4 Fluid mechanics (76-XX) 4 Biology and other natural sciences (92-XX) 3 Nonassociative rings and algebras (17-XX) 3 Real functions (26-XX) 3 Abstract harmonic analysis (43-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Systems theory; control (93-XX) 2 General algebraic systems (08-XX) 2 Commutative algebra (13-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Potential theory (31-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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