Edit Profile Bonatti, Christian Compute Distance To: Compute Author ID: bonatti.christian Published as: Bonatti, C.; Bonatti, Ch.; Bonatti, Christian Homepage: http://bonatti.perso.math.cnrs.fr/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND Documents Indexed: 130 Publications since 1985, including 3 Books all top 5 Co-Authors 11 single-authored 24 Díaz, Lorenzo Justiniano 16 Crovisier, Sylvain 15 Grines, Vyacheslav Zigmundovich 9 Viana, Marcelo 8 Pochinka, Olga Vital’evna 7 Wilkinson, Amie 6 Potrie, Rafael 5 Abdenur, Flavio 5 Bochi, Jairo 5 Gómez-Mont, Xavier 5 Medvedev, Vladislav Sergeevich 5 Pécou, Elisabeth 4 Béguin, François 4 Langevin, Rémi 4 Yang, Dawei 4 Zhang, Jinhua 3 Gan, Shaobo 3 Gourmelon, Nicolas 3 Guelman, Nancy 3 Shinohara, Katsutoshi 2 Gogolev, Andrey 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 Vago, Gioia Maria 2 Wen, Lan 1 Alvarez, Sébastien 1 Alves, José Ferreira 1 Arnaud, Marie-Claude 1 Baladi, Viviane 1 Baraviera, Alexandre Tavares 1 Bohnet, Doris 1 Bowden, Jonathan Peter 1 Da Luz, Adriana 1 Dolecki, Szymon 1 Dufraine, Emmanuel 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 Gorodetski, Anton 1 Hammerlindl, Andy 1 Kiriki, Shin 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 Rivas, Cristóbal 1 Rocha, Jorge 1 Schmitt, Bernard 1 Shilin, I. S. 1 Shilin, Ivan 1 Teixeira, Marco Antonto 1 Tresser, Charles 1 Triestino, Michele 1 Turcat, Gaël 1 Ures, Raúl 1 Vietez, J. L. 1 Vila Freyer, Ricardo Francisco 1 Villadelprat, Jordi 1 Vivier, Thérèse 1 Vuillemin, F. 1 Yu, Bin 1 Yu, Boming all top 5 Serials 22 Ergodic Theory and Dynamical Systems 7 Topology 5 Topology and its Applications 4 Israel Journal of Mathematics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Transactions of the American Mathematical Society 4 Journal of the Institute of Mathematics of Jussieu 3 Nonlinearity 3 Commentarii Mathematici Helvetici 3 Fundamenta Mathematicae 3 Publications Mathématiques 3 Inventiones Mathematicae 3 Mathematische Zeitschrift 3 Proceedings of the London Mathematical Society. Third Series 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 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 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 Dynamical and Control Systems 1 Moscow Mathematical Journal 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Astérisque 1 Ensaios Matemáticos 1 Groups, Geometry, and Dynamics 1 Electronic Research Announcements in Mathematical Sciences 1 Science China. Mathematics all top 5 Fields 114 Dynamical systems and ergodic theory (37-XX) 35 Manifolds and cell complexes (57-XX) 4 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 Topological groups, Lie groups (22-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 \(K\)-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 117 Publications have been cited 1,772 times in 835 Documents Cited by ▼ Year ▼ Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective. Zbl 1060.37020Bonatti, Christian; Díaz, Lorenzo J.; Viana, Marcelo 200 2005 SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Zbl 0962.37012Alves, José F.; Bonatti, Christian; Viana, Marcelo 129 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. 110 2003 Recurrence and genericity. Zbl 1071.37015Bonatti, Christian; Crovisier, Sylvain 105 2004 SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Zbl 0996.37033Bonatti, Christian; Viana, Marcelo 104 2000 Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms. Zbl 1246.37040Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 62 2011 Persistent nonhyperbolic transitive diffeomorphisms. Zbl 0852.58066Bonatti, Christian; Díaz, Lorenzo J. 61 1996 Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). Zbl 0959.37017Bonatti, C.; Grines, V. 41 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 38 2003 Perturbations of the derivative along periodic orbits. Zbl 1175.37027Bonatti, Christian; Gourmelon, Nikolas; Vivier, Thérèse 36 2006 Robust heterodimensional cycles and \(C^1\)-generic dynamics. Zbl 1156.37004Bonatti, Christian; Díaz, Lorenzo J. 33 2008 Periodic points and homoclinic classes. Zbl 1144.37007Abdenur, F.; Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wen, L. 31 2007 Removing zero Lyapunov exponents. Zbl 1048.37026Baraviera, Alexandre T.; Bonatti, Christian 29 2003 Transitive partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1074.57015Bonatti, Christian; Wilkinson, Amie 27 2005 Lorenz attractors with arbitrary expanding dimension. Zbl 0896.58043Bonatti, Christian; Pumariño, António; Viana, Marcelo 24 1997 Lyapunov exponents with multiplicity 1 for deterministic products of matrices. Zbl 1087.37017Bonatti, C.; Viana, M. 22 2004 On maximal transitive sets of generic diffeomorphisms. Zbl 1032.37011Bonatti, Christian; Dıaz, Lorenzo J. 21 2002 Topological classification of gradient-like diffeomorphisms on 3-manifolds. Zbl 1056.37023Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 20 2004 Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Zbl 1157.37309Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 20 2002 There is no “Shadowing lemma” for partially hyperbolic dynamics. Zbl 0973.37016Bonatti, Christian; Díaz, Lorenzo J.; Turcat, Gaël 20 2000 Abundance of \(C^{1}\)-robust homoclinic tangencies. Zbl 1300.37013Bonatti, Christian; Díaz, Lorenzo J. 19 2012 Towards a global view of dynamical systems, for the \(C^{1}\)-topology. Zbl 1256.37006Bonatti, C. 19 2011 Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms. Zbl 1031.37030Bonatti, Christian; Díaz, Lorenzo J.; Ures, Raúl 18 2002 Robust criterion for the existence of nonhyperbolic ergodic measures. Zbl 1368.37036Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. 17 2016 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. 17 2005 Non-hyperbolic ergodic measures with large support. Zbl 1195.37013Bonatti, Christian; Díaz, Lorenzo J.; Gorodetski, Anton 16 2010 Robustly transitive sets and heterodimensional cycles. Zbl 1056.37024Bonatti, Christian; Díaz, Lorenzo J.; Pujals, Enrique R.; Rocha, Jorge 16 2003 An example of transitive Anosov flows transversal to a torus and not conjugated to a suspension. Zbl 0826.58026Bonatti, Christian; Langevin, Remi 16 1994 Statistical behaviour of the leaves of certain holomorphic foliations. Zbl 1010.37025Bonatti, Christian; Gómez-Mont, Xavier 15 2001 Smale diffeomorphisms of surfaces. With the collab. of Emmanuelle Jeandenans. Zbl 0922.58058Bonatti, C.; Langevin, R. 15 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 15 1989 Stabilization of heterodimensional cycles. Zbl 1284.37020Bonatti, C.; Díaz, L. J.; Kiriki, S. 14 2012 Generic symplectic dynamics. Zbl 1084.37017Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain 14 2005 Non-wandering sets with non-empty interiors. Zbl 1083.37020Abdenur, Flavio; Bonatti, Christian; Díaz, Lorenzo J. 14 2004 Heteroclinic connections and genericity of infinitely many sinks and sources. Zbl 0944.37012Bonatti, Christian; Díaz, Lorenzo 14 1999 Perturbation of the Lyapunov spectra of periodic orbits. Zbl 1268.37027Bochi, J.; Bonatti, C. 12 2012 The \(C^1\) generic diffeomorphism has trivial centralizer. Zbl 1177.37025Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 12 2009 On the existence of non-trivial homoclinic classes. Zbl 1128.37021Bonatti, Christian; Gan, Shaobo; Wen, Lan 11 2007 Generic diffeomorphisms on compact surfaces. Zbl 1089.37032Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain; Díaz, Lorenzo J. 11 2005 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 Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics. Zbl 1362.37075Bohnet, Doris; Bonatti, Christian 10 2016 The \(C^{1+\alpha}\) hypothesis in Pesin theory revisited. Zbl 1312.37018Bonatti, Christian; Crovisier, Sylvain; Shinohara, Katsutoshi 10 2013 Local density of diffeomorphisms with large centralizers. Zbl 1163.58003Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie 10 2008 Smale flows in dimension 3: finite presentations of invariant neighbourhoods of saddle sets. Zbl 1102.37307Béguin, F.; Bonatti, C. 10 2002 Foliations in \(\mathbb{C} P(n)\): About hyperbolic holonomy for minimal exceptional sets. Zbl 0782.32023Bonatti, C.; Langevin, R.; Moussu, R. 10 1992 Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication. Zbl 1303.37008Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Gourmelon, N. 9 2013 Statistical behaviour of the leaves of Riccati foliations. Zbl 1209.37055Bonatti, Ch.; Gómez-Mont, X.; Vila-Freyer, R. 9 2010 On the hyperbolicity of homoclinic classes. Zbl 1200.37023Bonatti, Christian; Gan, Shaobo; Yang, Dawei 9 2009 Abnormal escape rates from nonuniformly hyperbolic sets. Zbl 0987.37018Baladi, Viviane; Bonatti, Christian; Schmitt, Bernard 9 1999 Rigidity for \(C^1\) actions on the interval arising from hyperbolicity. I: Solvable groups. Zbl 1433.37030Bonatti, C.; Monteverde, Ignacio; Navas, Andres; Rivas, Cristobal 8 2017 Robust vanishing of all Lyapunov exponents for iterated function systems. Zbl 1284.37044Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. 8 2014 Commuting analytic vector fields in dimension 3 or 4: Existence of common zeros. Zbl 0776.57013Bonatti, Christian 8 1992 Center manifolds for partially hyperbolic sets without strong unstable connections. Zbl 1362.37069Bonatti, Christian; Crovisier, Sylvain 7 2016 What is \(\ldots a\) blender? Zbl 1352.37075Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wilkinson, A. 7 2016 Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples. Zbl 1370.37069Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael 7 2016 Dominated Pesin theory: convex sum of hyperbolic measures. Zbl 1408.37054Bochi, Jairo; Bonatti, Christian; Gelfert, Katrin 6 2018 Axiom A diffeomorphisms derived from Anosov flows. Zbl 1201.37033Bonatti, Christian; Guelman, Nancy 6 2010 \(C^1\)-generic conservative diffeomorphisms have trivial centralizer. Zbl 1149.37017Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 6 2008 Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Zbl 1153.37340Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pochinka, O. V. 6 2007 Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds. Zbl 1222.37021Bonatti, Christian; Grines, Viacheslav; Pochinka, Olga 6 2006 Abundance of stable ergodicity. Zbl 1052.37023Bonatti, Christian; Matheus, Carlos; Viana, Marcelo; Wilkinson, Amie 6 2004 On Morse-Smale diffeomorphisms without heteroclinic intersections on three-manifolds. Zbl 1011.37013Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pécou, E. 6 2002 Two-dimensional links and diffeomorphisms on 3-manifolds. Zbl 1008.37013Bonatti, Christian; Grines, Viatcheslav; Pécou, Elisabeth 6 2002 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. 6 2001 Compact leaves of a generic codimension 1 foliation. Zbl 0828.57022Bonatti, Christian; Firmo, Sebastião 6 1994 Foliations near to a fibration. Zbl 1214.53022Bonatti, C. 6 1993 Déformations de feuilletages. (Deformations of foliations). Zbl 0703.57013Bonatti, C.; Haefliger, A. 6 1990 Building Anosov flows on 3-manifolds. Zbl 1375.37083Béguin, François; Bonatti, Christian; Yu, Bin 5 2017 Anomalous partially hyperbolic diffeomorphisms. I: Dynamically coherent examples. Zbl 1375.37093Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael 5 2016 Dominated chain recurrent class with singularities. Zbl 1371.37027Bonatti, Christian; Gan, Shaobo; Yang, Dawei 5 2015 A robustly chain transitive attractor with singularities of different indices. Zbl 1304.37002Bonatti, Christian; Li, Ming; Yang, Dawei 5 2013 On the existence of attractors. Zbl 1272.37019Bonatti, Christian; Li, Ming; Yang, Dawei 5 2013 Roots in the mapping class groups. Zbl 1160.57014Bonatti, Christian; Paris, Luis 5 2009 3-manifolds which are orbit spaces of diffeomorphisms. Zbl 1165.37001Bonatti, C.; Paoluzzi, L. 5 2008 Global dominated splittings and the \( C^1\) Newhouse phenomenon. Zbl 1088.37013Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 5 2006 Topological equivalence of saddle connections in dimension 3. Zbl 1056.37030Bonatti, Christian; Dufraine, Emmanuel 5 2003 Discontinuity of the Hausdorff dimension of hyperbolic sets. Zbl 0852.54038Bonatti, Christian; Díaz, Lorenzo Justiniano; Viana, Marcelo 5 1995 Wandering domains for infinitely renormalizable diffeomorphisms of the disk. Zbl 0843.57016Bonatti, Christian; Gambaudo, Jean Marc; Lion, Jean Marie; Tresser, Charles 5 1994 The index of holomorphic vector fields on singular varieties. I. Zbl 0810.32017Bonatti, Ch.; Gómez-Mont, X. 5 1994 Quasi-orbit spaces associated to \(T_0\)-spaces. Zbl 1218.54025Bonatti, C.; Hattab, H.; Salhi, E. 4 2011 Super exponential growth of the number of periodic orbits inside homoclinic classes. Zbl 1145.37015Bonatti, Christian; Díaz, Lorenzo J.; Fisher, Todd 4 2008 The index of stable critical points. Zbl 1013.37016Bonatti, Christian; Villadelprat, Jordi 4 2002 Dynamical systems in dimension 2 and 3: conjugacy invariants and classification. Zbl 1121.37306Bonatti, C.; Grines, V.; Langevin, R. 4 2001 Hyperbolicity as an obstruction to smoothability for one-dimensional actions. Zbl 1428.37029Bonatti, Christian; Lodha, Yash; Triestino, Michele 3 2019 Realization of Morse-Smale diffeomorphisms on 3-manifolds. Zbl 1377.37044Bonatti, Ch.; Grines, V. Z.; Pochinka, Olga V. 3 2017 Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1380.37065Bonatti, Christian; Zhang, Jinhua 3 2017 Hasse diagrams and orbit class spaces. Zbl 1213.54050Bonatti, C.; Hattab, H.; Salhi, E.; Vago, G. 3 2011 Transitive Anosov flows and Axiom-A diffeomorphisms. Zbl 1173.37028Bonatti, Christian; Guelman, Nancy 3 2009 A Hölder continuous vector field tangent to many foliations. Zbl 1147.37313Bonatti, Christian; Franks, John 3 2004 Recurrence and genericity. Zbl 1027.37011Bonatti, Christian; Crovisier, Sylvain 3 2003 Surface homeomorphisms with zero-dimensional singular set. Zbl 0929.37013Bonatti, C.; Kolev, B. 3 1998 Cubic tangencies and hyperbolic diffeomorphisms. Zbl 0943.37012Bonatti, Ch.; Díaz, L. J.; Vuillemin, F. 3 1998 Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds. Zbl 1435.37050Bonatti, C.; Grines, V.; Pochinka, O. 2 2019 Periodic measures and partially hyperbolic homoclinic classes. Zbl 1421.37018Bonatti, Christian; Zhang, Jinhua 2 2019 A criterion for zero averages and full support of ergodic measures. Zbl 07069469Bonatti, Christian; Díaz, Lorenzo J.; Bochi, Jairo 2 2018 Weak hyperbolic structures and robust properties of diffeomorphisms and flows. Zbl 1401.37037Bonatti, Christian; da Luz, Adriana 2 2018 Many intermingled basins in dimension 3. Zbl 1398.37017Bonatti, Christian; Potrie, Rafael 2 2018 Centralizers of \(C^1\)-contractions of the half line. Zbl 1326.22019Bonatti, Christian; Farinelli, Églantine 2 2015 Flexible periodic points. Zbl 1352.37076Bonatti, Christian; Shinohara, Katsutoshi 2 2015 Smooth conjugacy classes of circle diffeomorphisms with irrational rotation number. Zbl 1346.37045Bonatti, Christian; Guelman, Nancy 2 2014 Hyperbolicity as an obstruction to smoothability for one-dimensional actions. Zbl 1428.37029Bonatti, Christian; Lodha, Yash; Triestino, Michele 3 2019 Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds. Zbl 1435.37050Bonatti, C.; Grines, V.; Pochinka, O. 2 2019 Periodic measures and partially hyperbolic homoclinic classes. Zbl 1421.37018Bonatti, Christian; Zhang, Jinhua 2 2019 Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds. Zbl 1431.37032Bonatti, Ch.; Grines, V.; Laudenbach, F.; Pochinka, O. 1 2019 Dominated Pesin theory: convex sum of hyperbolic measures. Zbl 1408.37054Bochi, Jairo; Bonatti, Christian; Gelfert, Katrin 6 2018 A criterion for zero averages and full support of ergodic measures. Zbl 07069469Bonatti, Christian; Díaz, Lorenzo J.; Bochi, Jairo 2 2018 Weak hyperbolic structures and robust properties of diffeomorphisms and flows. Zbl 1401.37037Bonatti, Christian; da Luz, Adriana 2 2018 Many intermingled basins in dimension 3. Zbl 1398.37017Bonatti, Christian; Potrie, Rafael 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 8 2017 Building Anosov flows on 3-manifolds. Zbl 1375.37083Béguin, François; Bonatti, Christian; Yu, Bin 5 2017 Realization of Morse-Smale diffeomorphisms on 3-manifolds. Zbl 1377.37044Bonatti, Ch.; Grines, V. Z.; Pochinka, Olga V. 3 2017 Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1380.37065Bonatti, Christian; Zhang, Jinhua 3 2017 Existence of common zeros for commuting vector fields on three manifolds. 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. 17 2016 Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics. Zbl 1362.37075Bohnet, Doris; Bonatti, Christian 10 2016 Center manifolds for partially hyperbolic sets without strong unstable connections. Zbl 1362.37069Bonatti, Christian; Crovisier, Sylvain 7 2016 What is \(\ldots a\) blender? Zbl 1352.37075Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wilkinson, A. 7 2016 Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples. Zbl 1370.37069Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael 7 2016 Anomalous partially hyperbolic diffeomorphisms. I: Dynamically coherent examples. Zbl 1375.37093Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael 5 2016 Connectedness of the space of smooth actions of \(\mathbb{Z}^{n}\) on the interval. Zbl 1375.37081Bonatti, Christian; Eynard-Bontemps, Hélène 1 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 5 2015 Centralizers of \(C^1\)-contractions of the half line. Zbl 1326.22019Bonatti, Christian; Farinelli, Églantine 2 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. 8 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 10 2013 Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication. Zbl 1303.37008Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Gourmelon, N. 9 2013 A robustly chain transitive attractor with singularities of different indices. Zbl 1304.37002Bonatti, Christian; Li, Ming; Yang, Dawei 5 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. 19 2012 Stabilization of heterodimensional cycles. Zbl 1284.37020Bonatti, C.; Díaz, L. J.; Kiriki, S. 14 2012 Perturbation of the Lyapunov spectra of periodic orbits. Zbl 1268.37027Bochi, J.; Bonatti, C. 12 2012 Fragile cycles. Zbl 1279.37022Bonatti, Ch.; Díaz, L. J. 2 2012 Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms. Zbl 1246.37040Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 62 2011 Towards a global view of dynamical systems, for the \(C^{1}\)-topology. Zbl 1256.37006Bonatti, C. 19 2011 Quasi-orbit spaces associated to \(T_0\)-spaces. Zbl 1218.54025Bonatti, C.; Hattab, H.; Salhi, E. 4 2011 Hasse diagrams and orbit class spaces. Zbl 1213.54050Bonatti, C.; Hattab, H.; Salhi, E.; Vago, G. 3 2011 Non-hyperbolic ergodic measures with large support. Zbl 1195.37013Bonatti, Christian; Díaz, Lorenzo J.; Gorodetski, Anton 16 2010 Statistical behaviour of the leaves of Riccati foliations. Zbl 1209.37055Bonatti, Ch.; Gómez-Mont, X.; Vila-Freyer, R. 9 2010 Axiom A diffeomorphisms derived from Anosov flows. Zbl 1201.37033Bonatti, Christian; Guelman, Nancy 6 2010 The \(C^1\) generic diffeomorphism has trivial centralizer. Zbl 1177.37025Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 12 2009 On the hyperbolicity of homoclinic classes. Zbl 1200.37023Bonatti, Christian; Gan, Shaobo; Yang, Dawei 9 2009 Roots in the mapping class groups. Zbl 1160.57014Bonatti, Christian; Paris, Luis 5 2009 Transitive Anosov flows and Axiom-A diffeomorphisms. Zbl 1173.37028Bonatti, Christian; Guelman, Nancy 3 2009 Robust heterodimensional cycles and \(C^1\)-generic dynamics. Zbl 1156.37004Bonatti, Christian; Díaz, Lorenzo J. 33 2008 Local density of diffeomorphisms with large centralizers. Zbl 1163.58003Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie 10 2008 \(C^1\)-generic conservative diffeomorphisms have trivial centralizer. Zbl 1149.37017Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 6 2008 3-manifolds which are orbit spaces of diffeomorphisms. Zbl 1165.37001Bonatti, C.; Paoluzzi, L. 5 2008 Super exponential growth of the number of periodic orbits inside homoclinic classes. Zbl 1145.37015Bonatti, Christian; Díaz, Lorenzo J.; Fisher, Todd 4 2008 The centralizer of a \(C^1\)-generic diffeomorphism is trivial. Zbl 1149.37012Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie 2 2008 Periodic points and homoclinic classes. Zbl 1144.37007Abdenur, F.; Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wen, L. 31 2007 On the existence of non-trivial homoclinic classes. Zbl 1128.37021Bonatti, Christian; Gan, Shaobo; Wen, Lan 11 2007 Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Zbl 1153.37340Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pochinka, O. V. 6 2007 Perturbations of the derivative along periodic orbits. Zbl 1175.37027Bonatti, Christian; Gourmelon, Nikolas; Vivier, Thérèse 36 2006 Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds. Zbl 1222.37021Bonatti, Christian; Grines, Viacheslav; Pochinka, Olga 6 2006 Global dominated splittings and the \( C^1\) Newhouse phenomenon. Zbl 1088.37013Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain 5 2006 Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective. Zbl 1060.37020Bonatti, Christian; Díaz, Lorenzo J.; Viana, Marcelo 200 2005 Transitive partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1074.57015Bonatti, Christian; Wilkinson, Amie 27 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. 17 2005 Generic symplectic dynamics. 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. 11 2005 Recurrence and genericity. Zbl 1071.37015Bonatti, Christian; Crovisier, Sylvain 105 2004 Lyapunov exponents with multiplicity 1 for deterministic products of matrices. Zbl 1087.37017Bonatti, C.; Viana, M. 22 2004 Topological classification of gradient-like diffeomorphisms on 3-manifolds. Zbl 1056.37023Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 20 2004 Non-wandering sets with non-empty interiors. Zbl 1083.37020Abdenur, Flavio; Bonatti, Christian; Díaz, Lorenzo J. 14 2004 Abundance of stable ergodicity. Zbl 1052.37023Bonatti, Christian; Matheus, Carlos; Viana, Marcelo; Wilkinson, Amie 6 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. 110 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 38 2003 Removing zero Lyapunov exponents. Zbl 1048.37026Baraviera, Alexandre T.; Bonatti, Christian 29 2003 Robustly transitive sets and heterodimensional cycles. Zbl 1056.37024Bonatti, Christian; Díaz, Lorenzo J.; Pujals, Enrique R.; Rocha, Jorge 16 2003 Topological equivalence of saddle connections in dimension 3. Zbl 1056.37030Bonatti, Christian; Dufraine, Emmanuel 5 2003 Recurrence and genericity. Zbl 1027.37011Bonatti, Christian; Crovisier, Sylvain 3 2003 On maximal transitive sets of generic diffeomorphisms. Zbl 1032.37011Bonatti, Christian; Dıaz, Lorenzo J. 21 2002 Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Zbl 1157.37309Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E. 20 2002 Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms. Zbl 1031.37030Bonatti, Christian; Díaz, Lorenzo J.; Ures, Raúl 18 2002 Smale flows in dimension 3: finite presentations of invariant neighbourhoods of saddle sets. Zbl 1102.37307Béguin, F.; Bonatti, C. 10 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 Two-dimensional links and diffeomorphisms on 3-manifolds. Zbl 1008.37013Bonatti, Christian; Grines, Viatcheslav; Pécou, Elisabeth 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. 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. 6 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 129 2000 SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Zbl 0996.37033Bonatti, Christian; Viana, Marcelo 104 2000 Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). Zbl 0959.37017Bonatti, C.; Grines, V. 41 2000 There is no “Shadowing lemma” for partially hyperbolic dynamics. Zbl 0973.37016Bonatti, Christian; Díaz, Lorenzo J.; Turcat, Gaël 20 2000 Lorenz attractors with arbitrary expanding dimension. Zbl 0976.37014Bonatti, Ch.; Pumariño, A.; Viana, M. 2 2000 Heteroclinic connections and genericity of infinitely many sinks and sources. Zbl 0944.37012Bonatti, Christian; Díaz, Lorenzo 14 1999 Abnormal escape rates from nonuniformly hyperbolic sets. Zbl 0987.37018Baladi, Viviane; Bonatti, Christian; Schmitt, Bernard 9 1999 Construction of 3-dimensional Smale flows. Zbl 0966.37003Béguin, F.; Bonatti, C.; Vietez, J. L. 1 1999 Smale diffeomorphisms of surfaces. With the collab. of Emmanuelle Jeandenans. Zbl 0922.58058Bonatti, C.; Langevin, R. 15 1998 Surface homeomorphisms with zero-dimensional singular set. Zbl 0929.37013Bonatti, C.; Kolev, B. 3 1998 Cubic tangencies and hyperbolic diffeomorphisms. Zbl 0943.37012Bonatti, Ch.; Díaz, L. J.; Vuillemin, F. 3 1998 ...and 17 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 647 Authors 46 Bonatti, Christian 37 Grines, Vyacheslav Zigmundovich 35 Pochinka, Olga Vital’evna 29 Lee, Manseob 23 Varandas, Paulo 22 Morales, Carlos Arnoldo 21 Bessa, Mário 21 Viana, Marcelo 19 Alves, José Ferreira 19 Medvedev, Vladislav Sergeevich 18 Araújo, Vítor 17 Crovisier, Sylvain 17 Díaz, Lorenzo Justiniano 17 Potrie, Rafael 17 Zhuzhoma, Evgeniĭ Viktorovich 16 Yang, Jiagang 15 Bochi, Jairo 14 Gan, Shaobo 14 Gelfert, Katrin Grit 14 Yang, Dawei 11 Tahzibi, Ali 10 Avila Cordeiro de Melo, Artur 10 Hammerlindl, Andy 10 Pacifico, Maria José 10 Pinheiro, Vilton 10 Tian, Xueting 9 Arbieto, Alexander 9 Barrientos, Pablo G. 9 Rocha, Jorge 9 Zhou, Yunhua 8 Alvarez, Sébastien 8 Gurevich, Elena Ya. 8 Luzzatto, Stefano 8 Sambarino, Martín 8 Sumi, Naoya 8 Sun, Wenxiang 7 Fakhari, Abbas 7 Hirsch, Morris W. 7 Liang, Chao 7 Pesin, Yakov Borisovich 7 Pujals, Enrique Ramiro 7 Rams, Michał 7 Wen, Xiao 7 Zhang, Jinhua 6 Bautista, Serafín 6 Climenhaga, Vaughn 6 Dolgopyat, Dmitry 6 Fisher, Todd L. 6 Gorodetski, Anton 6 Homburg, Ale Jan 6 Liao, Gang 6 Oliveira, Krerley 6 Rodriguez-Hertz, Federico 6 Rodriguez Hertz, Jana 6 Shi, Yi 6 Ures, Raúl 6 Wang, Xiaodong 6 Zhu, Yujun 5 Andersson, Martin 5 Backes, Lucas H. 5 Béguin, François 5 Blonigan, Patrick J. 5 Cao, Yongluo 5 Castro, Armando 5 Catalan, Thiago 5 Catsigeras, Eleonora 5 Gogolev, Andrey 5 Gómez-Mont, Xavier 5 Gourmelon, Nicolas 5 Kleptsyn, Victor A. 5 Krauskopf, Bernd 5 Laudenbach, François 5 Lee, Keonhee 5 Lopes Dias, João 5 Osinga, Hinke Maria 5 Rodrigues, Alexandre A. P. 5 Saghin, Radu 5 Salgado, Luciana 5 Santiago, Bruno 5 Shinohara, Katsutoshi 5 Sibony, Nessim 5 Turaev, Dmitry V. 5 Vásquez, Carlos H. 5 Wen, Lan 5 Yu, Bin 4 Abdenur, Flavio 4 Asaoka, Masayuki 4 Barbot, Thierry 4 Berger, Pierre 4 Da Luz, Adriana 4 Fenley, Sérgio R. 4 Firmo, Sebatião 4 Freitas, Jorge Milhazes 4 Hattab, Hawete 4 Hittmeyer, Stefanie 4 Horita, Vanderlei 4 Ilyashenko, Yulij Sergeevich 4 Kiriki, Shin 4 Kuznetsov, Sergey P. 4 Li, Ming ...and 547 more Authors all top 5 Cited in 145 Serials 106 Ergodic Theory and Dynamical Systems 46 Discrete and Continuous Dynamical Systems 34 Proceedings of the American Mathematical Society 32 Journal of Differential Equations 31 Mathematische Zeitschrift 29 Dynamical Systems 27 Transactions of the American Mathematical Society 22 Communications in Mathematical Physics 20 Annales de l’Institut Henri Poincaré. 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Académie des Sciences, Paris 7 Chaos, Solitons and Fractals 7 Journal of Mathematical Sciences (New York) 7 Geometry & Topology 7 Regular and Chaotic Dynamics 6 Functional Analysis and its Applications 6 Doklady Mathematics 6 Journal of the European Mathematical Society (JEMS) 5 Journal of Mathematical Analysis and Applications 5 Duke Mathematical Journal 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Journal of the Institute of Mathematics of Jussieu 4 Journal of Computational Physics 4 Commentarii Mathematici Helvetici 4 Publications Mathématiques 4 Monatshefte für Mathematik 4 Physica D 4 Geometric and Functional Analysis. GAFA 4 Nonlinear Dynamics 4 Journal of Dynamical and Control Systems 4 Advances in Difference Equations 4 Science China. Mathematics 3 Russian Mathematical Surveys 3 Acta Mathematica 3 Journal of the Mathematical Society of Japan 3 Mathematische Annalen 3 Michigan Mathematical Journal 3 Chinese Annals of Mathematics. Series B 3 The Journal of Geometric Analysis 3 Boletim da Sociedade Brasileira de Matemática. Nova Série 3 Journal of Inequalities and Applications 3 Chaos 3 Annals of Mathematics. Second Series 3 Portugaliae Mathematica. Nova Série 3 Axioms 3 Open Mathematics 3 Journal de l’École Polytechnique – Mathématiques 2 Communications on Pure and Applied Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Fundamenta Mathematicae 2 Geometriae Dedicata 2 Journal für die Reine und Angewandte Mathematik 2 Proceedings of the London Mathematical Society. Third Series 2 Transactions of the Moscow Mathematical Society 2 Revista Matemática Iberoamericana 2 Journal of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 2 Topology Proceedings 2 Journal of Difference Equations and Applications 2 Annales Henri Poincaré 2 Differential Equations 2 Algebraic & Geometric Topology 2 SIAM Journal on Applied Dynamical Systems 1 Journal of Mathematical Physics 1 The Mathematical Intelligencer 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Colloquium Mathematicum 1 Compositio Mathematica 1 Indiana University Mathematics Journal 1 Journal of Geometry 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Quaestiones Mathematicae 1 SIAM Journal on Numerical Analysis 1 Tokyo Journal of Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Probability Theory and Related Fields ...and 45 more Serials all top 5 Cited in 42 Fields 771 Dynamical systems and ergodic theory (37-XX) 94 Manifolds and cell complexes (57-XX) 39 Ordinary differential equations (34-XX) 33 Differential geometry (53-XX) 29 Several complex variables and analytic spaces (32-XX) 28 General topology (54-XX) 25 Global analysis, analysis on manifolds (58-XX) 23 Measure and integration (28-XX) 18 Probability theory and stochastic processes (60-XX) 14 Group theory and generalizations (20-XX) 11 Mechanics of particles and systems (70-XX) 10 Functions of a complex variable (30-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Algebraic topology (55-XX) 6 Partial differential equations (35-XX) 5 Topological groups, Lie groups (22-XX) 5 Operator theory (47-XX) 4 Algebraic geometry (14-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Difference and functional equations (39-XX) 3 Nonassociative rings and algebras (17-XX) 3 Real functions (26-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Numerical analysis (65-XX) 3 Fluid mechanics (76-XX) 3 Systems theory; control (93-XX) 2 Mathematical logic and foundations (03-XX) 2 Commutative algebra (13-XX) 2 Abstract harmonic analysis (43-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-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 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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