Edit Profile (opens in new tab) Katok, Anatole Compute Distance To: Compute Author ID: katok.anatole Published as: Katok, Anatole; Katok, A.; Katok, A. B.; Katok, Anatole B.; Katok, Anatoly more...less Further Spellings: Katok, Anatoliĭ Borisovich; Каток Анатолий Борисович External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · GND · IdRef Documents Indexed: 130 Publications since 1964, including 11 Books 7 Contributions as Editor Biographic References: 7 Publications Co-Authors: 80 Co-Authors with 101 Joint Publications 2,662 Co-Co-Authors all top 5 Co-Authors 35 single-authored 13 Rodriguez-Hertz, Federico 9 Hasselblatt, Boris 7 Katok, Svetlana R. 7 Spatzier, Ralf J. 6 Damjanović, Danijela 6 Kalinin, Boris 6 Stëpin, Anatoliĭ Mikhaĭlovich 5 Anosov, Dmitriĭ Viktorovich 5 Fayad, Bassam R. 5 Pesin, Yakov Borisovich 4 Weiss, Howard 4 Zemlyakov, A. N. 3 Einsiedler, Manfred Leopold 3 Feres, Renato 3 Hurder, Steven E. 3 Knieper, Gerhard 3 Lemańczyk, Mariusz 3 Lewis, James Welsh 3 Niţică, Viorel 3 Sinaĭ, Yakov Grigor’evich 2 Brin, Michael 2 Burns, Keith 2 Climenhaga, Vaughn 2 Forni, Giovanni 2 Grines, Vyacheslav Zigmundovich 2 Gutkin, Eugene 2 Kozlov, Valeriĭ Vasil’evich 2 Neĭshtadt, Anatoliĭ Iserovich 2 Pollicott, Mark 2 Przytycki, Feliks 2 Schmidt, Klaus 2 Thouvenot, Jean-Paul 1 Afraimovich, Valentin S. 1 Aseev, Sergei M. 1 Bernstein, David 1 Bochi, Jairo 1 Bolibrukh, Andreĭ Andreevich 1 Bukhshtaber, Viktor Matveevich 1 Bunimovich, Leonid Abramovich 1 Davydov, Alekseĭ Aleksandrovich 1 de la Llave, Rafael 1 Erchenko, Alena 1 Feldman, Jacob 1 Flaminio, Livio 1 Foiaș, Ciprian 1 Gerber, Marlies 1 Gonchenko, Sergey V. 1 Grigorchuk, Rostislav Ivanovich 1 Gunesch, Roland 1 Gurevich, Boris 1 Ilyashenko, Yulij Sergeevich 1 Kashchenko, Sergeĭ Aleksandrovich 1 Kifer, Yuri 1 Klimenko, Alexey V. 1 Kononenko, Alexey 1 Krikorian, Raphaël 1 Kulikov, M. S. 1 Ledrappier, François 1 Leksin, Vladimir Pavlovich 1 Lerman, Lev 1 Lindenstrauss, Elon 1 Mezhirov, A. M. 1 Monastyrskiĭ, Mikhail Il’ich 1 Morozov, Al’bert Dmitrievich 1 Novikov, Sergeĭ Petrovich 1 Prikhod’ko, Aleksandr A. 1 Robinson, E. Arthur jun. 1 Samoĭlenko, Anatoliĭ Mykhaĭlovych 1 Sataev, A. B. 1 Sataev, Evgueni A. 1 Sharkovs’kyĭ, Oleksandr Mykolaĭovych 1 Shilnikov, Andrey L. 1 Strelcyn, Jean-Marie 1 Török, Andrei 1 Treshchev, Dmitriĭ Valer’evich 1 Turaev, Dmitry V. 1 Windsor, Alistair 1 Zakalyukin, Vladimir M. 1 Zelikin, Mikhail Il’ich 1 Zhirov, Aleksei Yu 1 Zhuzhoma, Evgeniĭ Viktorovich 1 Zimmer, Robert J. all top 5 Serials 18 Ergodic Theory and Dynamical Systems 7 Journal of Modern Dynamics 6 Uspekhi Matematicheskikh Nauk [N. S.] 6 Annals of Mathematics. Second Series 5 Israel Journal of Mathematics 5 Discrete and Continuous Dynamical Systems 3 Communications in Mathematical Physics 3 Mathematical Notes 3 Russian Mathematical Surveys 3 Fundamenta Mathematicae 3 Publications Mathématiques 3 Inventiones Mathematicae 3 Soviet Mathematics. Doklady 3 Mathematical Research Letters 2 Matematicheskie Zametki 2 Commentarii Mathematici Helvetici 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Mathematics of the USSR. Izvestiya 2 Bulletin of the American Mathematical Society. New Series 2 Electronic Research Announcements of the American Mathematical Society 2 Encyclopedia of Mathematics and Its Applications 2 Progress in Mathematics 2 Student Mathematical Library 1 Communications on Pure and Applied Mathematics 1 Journal d’Analyse Mathématique 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Geometriae Dedicata 1 Journal of Soviet Mathematics 1 Pacific Journal of Mathematics 1 Topology 1 Transactions of the Moscow Mathematical Society 1 Trudy Moskovskogo Matematicheskogo Obshchestva 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Notices of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Journal of Dynamical and Control Systems 1 Moscow Mathematical Journal 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Cambridge Tracts in Mathematics 1 Contemporary Mathematics 1 Lecture Notes in Mathematics 1 Proceedings of Symposia in Pure Mathematics 1 Translations. Series 2. American Mathematical Society 1 University Lecture Series 1 Electronic Research Announcements in Mathematical Sciences all top 5 Fields 108 Dynamical systems and ergodic theory (37-XX) 34 Measure and integration (28-XX) 17 Manifolds and cell complexes (57-XX) 13 Differential geometry (53-XX) 11 History and biography (01-XX) 10 Topological groups, Lie groups (22-XX) 10 General topology (54-XX) 8 General and overarching topics; collections (00-XX) 7 Global analysis, analysis on manifolds (58-XX) 4 Operator theory (47-XX) 3 Geometry (51-XX) 3 Mechanics of particles and systems (70-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Probability theory and stochastic processes (60-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 122 Publications have been cited 4,106 times in 2,901 Documents Cited by ▼ Year ▼ Introduction to the modern theory of dynamical systems. Zbl 0878.58020Katok, Anatole; Hasselblatt, Boris 1,227 1995 Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015Katok, A. 410 1980 Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019Katok, Anatole; Hasselblatt, Boris 101 1997 On local entropy. Zbl 0533.58020Brin, M.; Katok, A. 87 1983 Approximations in ergodic theory. Zbl 0172.07202Katok, A. B.; Stepin, A. M. 82 1967 Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001Katok, Anatole; Strelcyn, Jean-Marie 81 1986 A first course in dynamics with a panorama of recent developments. Zbl 1027.37001Hasselblatt, Boris; Katok, Anatole 76 2003 Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon 70 2006 Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021Katok, A. 68 1979 Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034Hurder, S.; Katok, A. 57 1990 Constructions in elliptic dynamics. Zbl 1089.37012Fayad, Bassam; Katok, Anatole 55 2004 First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027Katok, Anatole; Spatzier, Ralf J. 54 1994 Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021Katok, A.; Spatzier, R. J. 53 1996 Ergodic perturbations of degenerate integrable Hamiltonian systems. Zbl 0316.58010Katok, A. B. 53 1974 Entropy and closed geodesics. Zbl 0525.58027Katok, A. 52 1982 Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009Katok, Anatole 52 1980 Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001Katok, Anatole 47 2003 Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010Katok, A.; Spatzier, R. J. 43 1997 New examples in smooth ergodic theory. Ergodic diffeomorphisms. Zbl 0255.58007Anosov, D. V.; Katok, A. B. 43 1972 Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 42 1989 Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009Katok, Anatole; Thouvenot, Jean-Paul 41 1997 Topological transitivity of billiards in polygons. Zbl 0323.58012Zemlyakov, A. N.; Katok, A. B. 41 1976 Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029Katok, Anatole; Burns, Keith 38 1994 Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001Katok, Anatole 38 2007 Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048Katok, A. 36 1982 Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042Katok, Anatole 36 1988 Manifolds with non-positive curvature. Zbl 0572.58019Burns, K.; Katok, A. 35 1985 Handbook of dynamical systems. Volume 1A. Zbl 1013.00016 35 2002 Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040Bernstein, David; Katok, Anatole 34 1987 Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012Katok, A.; Lewis, J. 32 1991 Caustics for inner and outer billiards. Zbl 0839.58036Gutkin, Eugene; Katok, Anatole 31 1995 Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003Katok, Anatole; Robinson, E. A. jun. 31 2001 Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017Damjanović, Danijela; Katok, Anatole 30 2010 Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082Katok, A.; Kononenko, A. 30 1996 Invariant measures of flows on oriented surfaces. Zbl 0298.28013Katok, A. B. 30 1973 Neue Beispiele in der differenzierbaren Ergodentheorie. Ergodische Diffeomorphismen. Zbl 0218.58008Anosov, D. V.; Katok, A. B. 28 1970 The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020Katok, A. 27 1987 Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003Katok, Anatole; Nitică, Viorel 26 2011 Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005Katok, Anatole; Katok, Svetlana; Schmidt, Klaus 25 2002 Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026Katok, A.; Spatzier, R. J. 23 1994 Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304Katok, Anatole; Thouvenot, Jean-Paul 23 2006 Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016Kalinin, Boris; Katok, Anatole 23 2001 Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063Guysinsky, M.; Katok, A. 22 1998 Topologische Transitivität von Billards in Polygonen. Zbl 0315.58014Zemlyakov, A. N.; Katok, A. B. 21 1975 Principal structures. Zbl 1047.37001Hasselblatt, Boris; Katok, Anatole 20 2002 Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038Katok, A.; Lewis, J. 20 1996 Theory of dynamical systems and general transformation groups with invariant measure. Zbl 0399.28011Katok, A. B.; Sinai, Ya. G.; Stepin, A. M. 19 1975 Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041Katok, Anatole; Knieper, Gerhard; Weiss, Howard 19 1991 Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023Einsiedler, Manfred; Katok, Anatole 19 2003 Ergodic theory and Weil measures for foliations. Zbl 0645.57021Hurder, S.; Katok, A. 17 1987 Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017Einsiedler, Manfred; Katok, Anatole 17 2005 Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026Damjanovic, Danijela; Katok, Anatole 17 2011 Random perturbations of transformations of an interval. Zbl 0616.60064Katok, A.; Kifer, Y. 16 1986 Monotone equivalence in ergodic theory. Zbl 0379.28008Katok, A. B. 16 1977 Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029Damjanović, Danijela; Katok, Anatole 15 2005 Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039Katok, Anatole; Katok, Svetlana 15 1995 Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037Katok, A.; Lewis, J.; Zimmer, R. 14 1996 Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016Katok, A. 14 1980 Nonuniform measure rigidity. Zbl 1368.37031Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez 14 2011 Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021Brin, M. I.; Feldman, J.; Katok, A. 13 1981 Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029Gerber, Marlies; Katok, Anatole 12 1982 Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042Katok, Anatole; Niţică, Viorel; Török, Andrei 12 2000 Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on \(\mathrm{SL}(n,\mathbb R)/\Gamma \). Zbl 1291.37027Damjanović, Danijela; Katok, Anatole 12 2011 Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017Kalinin, Boris; Katok, Anatole 11 2007 Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005Katok, A.; Lemańczyk, M. 10 2009 Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029Feres, Renato; Katok, Anatole 10 2002 Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032Katok, A. 9 1983 Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023Katok, Anatole; Katok, Svetlana 9 2005 Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050Feres, Renato; Katok, Anatoly 9 1989 Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. With an appendix by Alex Furman. Zbl 1009.37013Gunesch, Roland; Katok, Anatole B. 9 2000 Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039Feres, Renato; Katok, Anatole 9 1990 Approximation of ergodic dynamical systems by periodic transformations. Zbl 0186.46701Katok, A. B.; Stepin, A. M. 9 1966 Metric properties of homeomorphisms which preserve the measure. Zbl 0198.55701Katok, A. B.; Stepin, A. M. 9 1970 Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024Katok, A. 8 1992 The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015Katok, Anatole B.; Schmidt, Klaus 8 1995 Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021Fayad, Bassam; Katok, Anatole 8 2014 The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico 8 2014 Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 8 1990 Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001Katok, Anatole; Climenhaga, Vaughn 8 2008 Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083Erchenko, Alena; Katok, Anatole 8 2019 Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300Fayad, Bassam; Katok, Anatole; Windsor, Alistar 8 2001 Metric properties of measure preserving homeomorphisms. Zbl 0209.27803Katok, A. B.; Stepin, A. M. 8 1970 Time change, monotone equivalent and standard dynamical systems. Zbl 0326.28025Katok, A. B. 8 1975 Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015Hurder, S.; Katok, A. 7 1984 Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037Katok, Anatole; Hertz, Federico Rodriguez 7 2010 Handbook of dynamical systems. Volume 1B. Zbl 1081.00006 7 2006 Spectral properties of dynamical systems with an integral invariant on the torus. Zbl 0172.12102Katok, A. B. 6 1967 Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020Katok, A. B. 6 1977 Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048Katok, Anatole; Rodriguez Hertz, Federico 6 2016 Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029Kalinin, Boris; Katok, Anatole 6 2002 Dynamical systems with hyperbolic structure. Zbl 0598.58031Katok, A. B. 5 1981 Standardness of automorphisms of transposition of intervals and fluxes on surfaces. Zbl 0368.58010Katok, A. B.; Sataev, A. B. 5 1976 Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015Damjanović, Danijela; Katok, Anatole 5 2004 Rigidity of real-analytic actions of \(SL(n,\mathbb Z)\) on \(\mathbb T^n\): a case of realization of Zimmer program. Zbl 1192.37025Katok, Anatole; Hertz, Federico Rodriguez 5 2010 Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017Katok, A.; Niţică, V. 5 2007 Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002Katok, Anatole 5 1996 Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033Flaminio, L.; Katok, A. 5 1992 Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data. Zbl 1136.37016Katok, Anatole; Rodriguez Hertz, Federico 5 2007 Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016Katok, Anatole 4 1984 A conjecture about entropy. Zbl 0628.58026Katok, A. B. 4 1977 Flexibility of Lyapunov exponents. Zbl 1495.37024Bochi, J.; Katok, A.; Rodriguez Hertz, F. 1 2022 Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083Erchenko, Alena; Katok, Anatole 8 2019 Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002 4 2017 From groups to geometry and back. Zbl 1428.20001Climenhaga, Vaughn; Katok, Anatole 2 2017 Dmitry Viktorovich Anosov: his life and mathematics. Zbl 1386.01011Katok, Anatole 1 2017 Non-uniform measure rigidity for \(\mathbb{Z}^k\) actions of symplectic type. Zbl 1388.37032Katok, Anatole; Rodriguez Hertz, Federico 1 2017 Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048Katok, Anatole; Rodriguez Hertz, Federico 6 2016 Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021Fayad, Bassam; Katok, Anatole 8 2014 The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico 8 2014 Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003Katok, Anatole; Nitică, Viorel 26 2011 Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026Damjanovic, Danijela; Katok, Anatole 17 2011 Nonuniform measure rigidity. Zbl 1368.37031Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez 14 2011 Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on \(\mathrm{SL}(n,\mathbb R)/\Gamma \). Zbl 1291.37027Damjanović, Danijela; Katok, Anatole 12 2011 Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017Damjanović, Danijela; Katok, Anatole 30 2010 Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037Katok, Anatole; Hertz, Federico Rodriguez 7 2010 Rigidity of real-analytic actions of \(SL(n,\mathbb Z)\) on \(\mathbb T^n\): a case of realization of Zimmer program. Zbl 1192.37025Katok, Anatole; Hertz, Federico Rodriguez 5 2010 Errata to “Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on Tori” and “Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data”. Zbl 1192.37026Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez 3 2010 Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005Katok, A.; Lemańczyk, M. 10 2009 Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001Katok, Anatole; Climenhaga, Vaughn 8 2008 New progress in nonuniform measure and cocycle rigidity. Zbl 1159.37316Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez 4 2008 Moscow dynamics seminars of the nineteen seventies and the early career of Yasha Pesin. Zbl 1152.01009Katok, Anatole 3 2008 Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001Katok, Anatole 38 2007 Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017Kalinin, Boris; Katok, Anatole 11 2007 Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017Katok, A.; Niţică, V. 5 2007 Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data. Zbl 1136.37016Katok, Anatole; Rodriguez Hertz, Federico 5 2007 Local rigidity of restrictions of Weyl chamber flows. Zbl 1113.37015Damjanović, Danijela; Katok, Anatole 3 2007 Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon 70 2006 Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304Katok, Anatole; Thouvenot, Jean-Paul 23 2006 Handbook of dynamical systems. Volume 1B. Zbl 1081.00006 7 2006 Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017Einsiedler, Manfred; Katok, Anatole 17 2005 Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029Damjanović, Danijela; Katok, Anatole 15 2005 Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023Katok, Anatole; Katok, Svetlana 9 2005 Billiard table as a playground for a mathematician. Zbl 1147.37329Katok, A. B. 4 2005 Constructions in elliptic dynamics. Zbl 1089.37012Fayad, Bassam; Katok, Anatole 55 2004 Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015Damjanović, Danijela; Katok, Anatole 5 2004 A first course in dynamics with a panorama of recent developments. Zbl 1027.37001Hasselblatt, Boris; Katok, Anatole 76 2003 Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001Katok, Anatole 47 2003 Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023Einsiedler, Manfred; Katok, Anatole 19 2003 Handbook of dynamical systems. Volume 1A. Zbl 1013.00016 35 2002 Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005Katok, Anatole; Katok, Svetlana; Schmidt, Klaus 25 2002 Principal structures. Zbl 1047.37001Hasselblatt, Boris; Katok, Anatole 20 2002 Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029Feres, Renato; Katok, Anatole 10 2002 Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029Kalinin, Boris; Katok, Anatole 6 2002 The development of dynamics in the 20th century and the contribution of Jürgen Moser. Zbl 1018.37001Hasselblatt, Boris; Katok, Anatole 2 2002 Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003Katok, Anatole; Robinson, E. A. jun. 31 2001 Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016Kalinin, Boris; Katok, Anatole 23 2001 Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300Fayad, Bassam; Katok, Anatole; Windsor, Alistar 8 2001 Smooth ergodic theory and its applications. Proceedings of the AMS summer research institute, Seattle, WA, USA, July 26–August 13, 1999. Zbl 0973.00044 2 2001 Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042Katok, Anatole; Niţică, Viorel; Török, Andrei 12 2000 Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. With an appendix by Alex Furman. Zbl 1009.37013Gunesch, Roland; Katok, Anatole B. 9 2000 Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063Guysinsky, M.; Katok, A. 22 1998 Entropy and growth of expanding periodic orbits for one-dimensional maps. Zbl 0915.58025Katok, A.; Mezhirov, A. 1 1998 Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019Katok, Anatole; Hasselblatt, Boris 101 1997 Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010Katok, A.; Spatzier, R. J. 43 1997 Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009Katok, Anatole; Thouvenot, Jean-Paul 41 1997 Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021Katok, A.; Spatzier, R. J. 53 1996 Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082Katok, A.; Kononenko, A. 30 1996 Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038Katok, A.; Lewis, J. 20 1996 Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037Katok, A.; Lewis, J.; Zimmer, R. 14 1996 Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002Katok, Anatole 5 1996 Nonstationary normal forms and rigidity of group actions. Zbl 0871.58073Katok, A.; Spatzier, R. J. 3 1996 Introduction to the modern theory of dynamical systems. Zbl 0878.58020Katok, Anatole; Hasselblatt, Boris 1,227 1995 Caustics for inner and outer billiards. Zbl 0839.58036Gutkin, Eugene; Katok, Anatole 31 1995 Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039Katok, Anatole; Katok, Svetlana 15 1995 The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015Katok, Anatole B.; Schmidt, Klaus 8 1995 First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027Katok, Anatole; Spatzier, Ralf J. 54 1994 Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029Katok, Anatole; Burns, Keith 38 1994 Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026Katok, A.; Spatzier, R. J. 23 1994 Women in Soviet mathematics. Zbl 1194.01176Katok, Anatole; Katok, Svetlana 3 1993 Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024Katok, A. 8 1992 Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033Flaminio, L.; Katok, A. 5 1992 Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012Katok, A.; Lewis, J. 32 1991 Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041Katok, Anatole; Knieper, Gerhard; Weiss, Howard 19 1991 Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034Hurder, S.; Katok, A. 57 1990 Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039Feres, Renato; Katok, Anatole 9 1990 Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 8 1990 Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 42 1989 Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050Feres, Renato; Katok, Anatoly 9 1989 Vladimir Abramovich Rokhlin (23 August 1919 to 3 December 1984): Introductory note. Zbl 0688.01012Katok, A. 1 1989 Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042Katok, Anatole 36 1988 Weakly mixing billiards. Zbl 0673.58028Gutkin, E.; Katok, A. 2 1988 Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040Bernstein, David; Katok, Anatole 34 1987 The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020Katok, A. 27 1987 Ergodic theory and Weil measures for foliations. Zbl 0645.57021Hurder, S.; Katok, A. 17 1987 Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001Katok, Anatole; Strelcyn, Jean-Marie 81 1986 Random perturbations of transformations of an interval. Zbl 0616.60064Katok, A.; Kifer, Y. 16 1986 Manifolds with non-positive curvature. Zbl 0572.58019Burns, K.; Katok, A. 35 1985 Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015Hurder, S.; Katok, A. 7 1984 Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016Katok, Anatole 4 1984 On local entropy. Zbl 0533.58020Brin, M.; Katok, A. 87 1983 Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032Katok, A. 9 1983 Entropy and closed geodesics. Zbl 0525.58027Katok, A. 52 1982 Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048Katok, A. 36 1982 Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029Gerber, Marlies; Katok, Anatole 12 1982 Ergodic theory and dynamical systems II. Proceedings, special year, Maryland 1979-80. Zbl 0483.00005 1 1982 Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021Brin, M. I.; Feldman, J.; Katok, A. 13 1981 Dynamical systems with hyperbolic structure. Zbl 0598.58031Katok, A. B. 5 1981 Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015Katok, A. 410 1980 Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009Katok, Anatole 52 1980 Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016Katok, A. 14 1980 ...and 22 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,567 Authors 35 Katok, Anatole 23 Pesin, Yakov Borisovich 21 Barreira, Luis Manuel 21 de la Llave, Rafael 21 Einsiedler, Manfred Leopold 20 Varandas, Paulo 19 Lindenstrauss, Elon 19 Morales, Carlos Arnoldo 19 Pollicott, Mark 19 Sun, Wenxiang 18 Fayad, Bassam R. 18 Rodriguez-Hertz, Federico 17 Gelfert, Katrin Grit 16 Chen, Ercai 16 Forni, Giovanni 16 Oertel-Jäger, Tobias Hendrik 16 Kanigowski, Adam 16 Kuznetsov, Sergey P. 16 Lemańczyk, Mariusz 16 Mesón, Alejandro M. 16 Troubetzkoy, Serge Eugene 16 Valls Anglés, Cláudia 16 Vericat, Fernando 15 Huang, Wen 15 Kalinin, Boris 15 Paternain, Gabriel Pedro 15 Sadovskaya, Victoria 15 Young, Lai-Sang 15 Zhao, Yun 14 Climenhaga, Vaughn 14 Damjanović, Danijela 14 Gutkin, Eugene 14 Hasselblatt, Boris 14 Ledrappier, François 14 Mihailescu, Eugen Gh. 14 Ryzhikov, Valeriĭ Valentinovich 14 Yang, Jiagang 13 Buzzi, Jérôme 13 Cao, Yongluo 13 Crovisier, Sylvain 13 Dolgopyat, Dmitry 13 Frączek, Krzysztof Marek 13 Spatzier, Ralf J. 12 Avila, Artur 12 Chaika, Jonathan 12 Duan, Huagui 12 Knieper, Gerhard 12 Kunde, Philipp 12 Stoyanov, Luchezar N. 11 Baladi, Viviane 11 Bonatti, Christian 11 Bunimovich, Leonid Abramovich 11 Dragičević, Davor 11 Ferenczi, Sébastien 11 Kolesov, Andreĭ Yur’evich 11 Wilkinson, Amie 11 Ye, Xiangdong 10 Glyzin, Sergeĭ Dmitrievich 10 Guillarmou, Colin 10 Long, Yiming 10 Tian, Xueting 10 Tien Cuong Dinh 10 Weiss, Howard 10 Zhou, Yunhua 9 Araújo, Vítor 9 Chernov, Nikolai Ivanovich 9 Hurder, Steven E. 9 Kawan, Christoph 9 Le Calvez, Patrice 9 Llibre, Jaume 9 Masur, Howard A. 9 Potrie, Rafael 9 Rozov, Nikolaĭ Khristovich 9 Shu, Lin 9 Sibony, Nessim 9 Wang, Zhenqi Jenny 9 Zhu, Yujun 8 Andres, Jan 8 Backes, Lucas H. 8 Bessa, Mário 8 Biś, Andrzej 8 Burns, Keith 8 Cheng, Wenchiao 8 de Thélin, Henry 8 Díaz, Lorenzo Justiniano 8 Gerber, Marlies 8 Giona, Massimiliano 8 Gogolev, Andrey 8 Gorodetskii, Anton Semenovich 8 Hubert, Pascal 8 Labourie, François 8 Lian, Zeng 8 Liang, Chao 8 Liao, Gang 8 Liverani, Carlangelo 8 Rodriguez Hertz, Jana 8 Tahzibi, Ali 8 Thompson, Daniel J. 8 Ulcigrai, Corinna 8 Vetokhin, Alexandr N. ...and 2,467 more Authors all top 5 Cited in 375 Serials 254 Ergodic Theory and Dynamical Systems 106 Communications in Mathematical Physics 98 Discrete and Continuous Dynamical Systems 97 Israel Journal of Mathematics 92 Transactions of the American Mathematical Society 85 Proceedings of the American Mathematical Society 78 Journal of Statistical Physics 72 Journal of Differential Equations 63 Inventiones Mathematicae 60 Physica D 56 Advances in Mathematics 47 Annales de l’Institut Fourier 46 Journal of Modern Dynamics 43 Duke Mathematical Journal 42 Dynamical Systems 38 Journal of Mathematical Analysis and Applications 33 Mathematische Zeitschrift 32 Annals of Mathematics. Second Series 31 Journal d’Analyse Mathématique 30 Journal of Dynamics and Differential Equations 30 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 29 Mathematical Notes 29 Mathematische Annalen 28 Nonlinearity 27 Topology and its Applications 26 Chaos, Solitons and Fractals 25 Geometric and Functional Analysis. GAFA 24 Bulletin of the American Mathematical Society. New Series 24 Journal of Mathematical Sciences (New York) 24 Chaos 24 Regular and Chaotic Dynamics 23 Geometriae Dedicata 23 Qualitative Theory of Dynamical Systems 21 Functional Analysis and its Applications 21 Journal of Functional Analysis 21 Journal of the European Mathematical Society (JEMS) 20 Journal of the American Mathematical Society 20 Proceedings of the Steklov Institute of Mathematics 19 Geometry & Topology 19 Acta Mathematica Sinica. English Series 17 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 17 Journal of Dynamical and Control Systems 17 Comptes Rendus. 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A 11 Publications Mathématiques 11 Calculus of Variations and Partial Differential Equations 10 Journal of Geometry and Physics 10 Journal of Nonlinear Science 10 Electronic Research Announcements of the American Mathematical Society 10 Journal of Fixed Point Theory and Applications 9 Bulletin de la Société Mathématique de France 9 The Journal of Geometric Analysis 9 Differential Equations 9 Discrete and Continuous Dynamical Systems. Series B 8 Journal of Mathematical Physics 8 Compositio Mathematica 8 Theoretical Computer Science 8 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 8 Journal of Dynamical Systems and Geometric Theories 7 Automatica 7 Memoirs of the American Mathematical Society 7 Differential Geometry and its Applications 7 Experimental Mathematics 7 Journal of Topology and Analysis 6 Fundamenta Mathematicae 6 Annales de l’Institut Henri Poincaré. Physique Théorique 6 Conformal Geometry and Dynamics 6 Communications in Nonlinear Science and Numerical Simulation 6 Algebraic & Geometric Topology 6 Journal de l’École Polytechnique – Mathématiques 6 Russian Journal of Nonlinear Dynamics 5 Journal of Mathematical Biology 5 Acta Mathematica 5 Results in Mathematics 5 Transactions of the Moscow Mathematical Society 5 Systems & Control Letters 5 Linear Algebra and its Applications 5 Stochastic Processes and their Applications 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Boletim da Sociedade Brasileira de Matemática. Nova Série 5 Russian Mathematics 5 Acta Mathematica Scientia. Series B. (English Edition) 5 Entropy 5 Journal of the Institute of Mathematics of Jussieu 5 Discrete and Continuous Dynamical Systems. Series S 5 Arnold Mathematical Journal 4 Archive for Rational Mechanics and Analysis 4 Journal of Computational Physics 4 Moscow University Mathematics Bulletin ...and 275 more Serials all top 5 Cited in 63 Fields 2,369 Dynamical systems and ergodic theory (37-XX) 318 Differential geometry (53-XX) 301 Measure and integration (28-XX) 162 Ordinary differential equations (34-XX) 154 Manifolds and cell complexes (57-XX) 147 Global analysis, analysis on manifolds (58-XX) 134 General topology (54-XX) 122 Topological groups, Lie groups (22-XX) 112 Number theory (11-XX) 112 Probability theory and stochastic processes (60-XX) 105 Mechanics of particles and systems (70-XX) 101 Several complex variables and analytic spaces (32-XX) 82 Partial differential equations (35-XX) 79 Statistical mechanics, structure of matter (82-XX) 69 Operator theory (47-XX) 62 Group theory and generalizations (20-XX) 56 Functions of a complex variable (30-XX) 53 Quantum theory (81-XX) 49 Systems theory; control (93-XX) 45 Computer science (68-XX) 35 Functional analysis (46-XX) 34 Information and communication theory, circuits (94-XX) 33 Biology and other natural sciences (92-XX) 32 Numerical analysis (65-XX) 32 Fluid mechanics (76-XX) 28 Algebraic geometry (14-XX) 25 Combinatorics (05-XX) 23 Difference and functional equations (39-XX) 21 Convex and discrete geometry (52-XX) 19 Algebraic topology (55-XX) 18 Real functions (26-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 Abstract harmonic analysis (43-XX) 16 Geometry (51-XX) 14 Statistics (62-XX) 10 General and overarching topics; collections (00-XX) 10 History and biography (01-XX) 10 Mathematical logic and foundations (03-XX) 10 \(K\)-theory (19-XX) 9 Optics, electromagnetic theory (78-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Geophysics (86-XX) 7 Mechanics of deformable solids (74-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Operations research, mathematical programming (90-XX) 6 Associative rings and algebras (16-XX) 6 Potential theory (31-XX) 5 Category theory; homological algebra (18-XX) 4 Special functions (33-XX) 4 Relativity and gravitational theory (83-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Commutative algebra (13-XX) 3 Integral transforms, operational calculus (44-XX) 2 General algebraic systems (08-XX) 2 Nonassociative rings and algebras (17-XX) 2 Integral equations (45-XX) 2 Astronomy and astrophysics (85-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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