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 100 Joint Publications 2,610 Co-Co-Authors all top 5 Co-Authors 36 single-authored 12 Rodriguez-Hertz, Federico 8 Hasselblatt, Boris 6 Damjanović, Danijela 6 Kalinin, Boris 6 Katok, Svetlana R. 6 Spatzier, Ralf J. 6 Stepin, Anatolii Mikhailovich 5 Anosov, Dmitriĭ Viktorovich 4 Fayad, Bassam R. 4 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 Lewis, James Welsh 3 Niţică, Viorel 3 Sinaĭ, Yakov Grigor’evich 2 Brin, Michael 2 Burns, Keith 2 Climenhaga, Vaughn 2 Grines, Vyacheslav Zigmundovich 2 Gutkin, Eugene 2 Kozlov, Valeriĭ Vasil’evich 2 Lemańczyk, Mariusz 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 Foiaş, Ciprian Ilie 1 Forni, Giovanni 1 Gerber, Marlies 1 Gonchenko, Sergey V. 1 Grigorchuk, Rostislav Ivanovich 1 Gunesch, Roland 1 Gurevich, B. M. 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 3,901 times in 2,777 Documents Cited by ▼ Year ▼ Introduction to the modern theory of dynamical systems. Zbl 0878.58020Katok, Anatole; Hasselblatt, Boris 1,177 1995 Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015Katok, A. 387 1980 Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019Katok, Anatole; Hasselblatt, Boris 99 1997 On local entropy. Zbl 0533.58020Brin, M.; Katok, A. 83 1983 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 78 1986 Approximations in ergodic theory. Zbl 0172.07202Katok, A. B.; Stepin, A. M. 78 1967 A first course in dynamics with a panorama of recent developments. Zbl 1027.37001Hasselblatt, Boris; Katok, Anatole 73 2003 Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon 69 2006 Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021Katok, A. 66 1979 Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034Hurder, S.; Katok, A. 54 1990 First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027Katok, Anatole; Spatzier, Ralf J. 52 1994 Ergodic perturbations of degenerate integrable Hamiltonian systems. Zbl 0316.58010Katok, A. B. 52 1974 Constructions in elliptic dynamics. Zbl 1089.37012Fayad, Bassam; Katok, Anatole 51 2004 Entropy and closed geodesics. Zbl 0525.58027Katok, A. 48 1982 Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021Katok, A.; Spatzier, R. J. 46 1996 Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009Katok, Anatole 46 1980 Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001Katok, Anatole 43 2003 Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009Katok, Anatole; Thouvenot, Jean-Paul 41 1997 Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 40 1989 Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010Katok, A.; Spatzier, R. J. 40 1997 New examples in smooth ergodic theory. Ergodic diffeomorphisms. Zbl 0255.58007Anosov, D. V.; Katok, A. B. 40 1972 Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029Katok, Anatole; Burns, Keith 36 1994 Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042Katok, Anatole 36 1988 Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001Katok, Anatole 36 2007 Topological transitivity of billiards in polygons. Zbl 0323.58012Zemlyakov, A. N.; Katok, A. B. 35 1976 Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048Katok, A. 33 1982 Manifolds with non-positive curvature. Zbl 0572.58019Burns, K.; Katok, A. 33 1985 Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040Bernstein, David; Katok, Anatole 32 1987 Handbook of dynamical systems. Volume 1A. Zbl 1013.00016 32 2002 Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012Katok, A.; Lewis, J. 31 1991 Invariant measures of flows on oriented surfaces. Zbl 0298.28013Katok, A. B. 30 1973 Caustics for inner and outer billiards. Zbl 0839.58036Gutkin, Eugene; Katok, Anatole 28 1995 Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003Katok, Anatole; Robinson, E. A. jun. 28 2001 Neue Beispiele in der differenzierbaren Ergodentheorie. Ergodische Diffeomorphismen. Zbl 0218.58008Anosov, D. V.; Katok, A. B. 28 1970 Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082Katok, A.; Kononenko, A. 27 1996 The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020Katok, A. 27 1987 Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017Damjanović, Danijela; Katok, Anatole 25 2010 Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003Katok, Anatole; Nitică, Viorel 25 2011 Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016Kalinin, Boris; Katok, Anatole 23 2001 Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026Katok, A.; Spatzier, R. J. 22 1994 Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005Katok, Anatole; Katok, Svetlana; Schmidt, Klaus 22 2002 Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304Katok, Anatole; Thouvenot, Jean-Paul 22 2006 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 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 Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023Einsiedler, Manfred; Katok, Anatole 18 2003 Ergodic theory and Weil measures for foliations. Zbl 0645.57021Hurder, S.; Katok, A. 17 1987 Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041Katok, Anatole; Knieper, Gerhard; Weiss, Howard 17 1991 Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017Einsiedler, Manfred; Katok, Anatole 16 2005 Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026Damjanovic, Danijela; Katok, Anatole 16 2011 Principal structures. Zbl 1047.37001Hasselblatt, Boris; Katok, Anatole 16 2002 Random perturbations of transformations of an interval. Zbl 0616.60064Katok, A.; Kifer, Y. 15 1986 Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039Katok, Anatole; Katok, Svetlana 14 1995 Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037Katok, A.; Lewis, J.; Zimmer, R. 14 1996 Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029Damjanović, Danijela; Katok, Anatole 14 2005 Nonuniform measure rigidity. Zbl 1368.37031Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez 14 2011 Monotone equivalence in ergodic theory. Zbl 0379.28008Katok, A. B. 14 1977 Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042Katok, Anatole; Niţică, Viorel; Török, Andrei 12 2000 Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016Katok, A. 12 1980 Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021Brin, M. I.; Feldman, J.; Katok, A. 12 1981 Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029Gerber, Marlies; Katok, Anatole 12 1982 Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005Katok, A.; Lemańczyk, M. 10 2009 Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017Kalinin, Boris; Katok, Anatole 10 2007 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 10 2011 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 Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023Katok, Anatole; Katok, Svetlana 9 2005 Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032Katok, A. 9 1983 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 Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029Feres, Renato; Katok, Anatole 9 2002 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 The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015Katok, Anatole B.; Schmidt, Klaus 8 1995 Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050Feres, Renato; Katok, Anatoly 8 1989 Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024Katok, A. 8 1992 Time change, monotone equivalent and standard dynamical systems. Zbl 0326.28025Katok, A. B. 8 1975 Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300Fayad, Bassam; Katok, Anatole; Windsor, Alistar 8 2001 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 Metric properties of measure preserving homeomorphisms. Zbl 0209.27803Katok, A. B.; Stepin, A. M. 8 1970 Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001Katok, Anatole; Climenhaga, Vaughn 8 2008 Handbook of dynamical systems. Volume 1B. Zbl 1081.00006 7 2006 Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 7 1990 Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048Katok, Anatole; Rodriguez Hertz, Federico 6 2016 Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037Katok, Anatole; Hertz, Federico Rodriguez 6 2010 Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029Kalinin, Boris; Katok, Anatole 6 2002 Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021Fayad, Bassam; Katok, Anatole 6 2014 Spectral properties of dynamical systems with an integral invariant on the torus. Zbl 0172.12102Katok, A. B. 6 1967 Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083Erchenko, Alena; Katok, Anatole 6 2019 Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002Katok, Anatole 5 1996 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 symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033Flaminio, L.; Katok, A. 5 1992 Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017Katok, A.; Niţică, V. 5 2007 Standardness of automorphisms of transposition of intervals and fluxes on surfaces. Zbl 0368.58010Katok, A. B.; Sataev, A. B. 5 1976 Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020Katok, A. B. 5 1977 Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015Hurder, S.; Katok, A. 5 1984 Dynamical systems with hyperbolic structure. Zbl 0598.58031Katok, A. B. 5 1981 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 actions of higher rank abelian groups and KAM method. Zbl 1068.37015Damjanović, Danijela; Katok, Anatole 5 2004 A conjecture about entropy. Zbl 0628.58026Katok, A. B. 4 1977 Billiard table as a playground for a mathematician. Zbl 1147.37329Katok, A. B. 4 2005 Flexibility of Lyapunov exponents. Zbl 07457816Bochi, J.; Katok, A.; Rodriguez Hertz, F. 1 2022 Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083Erchenko, Alena; Katok, Anatole 6 2019 Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002 3 2017 From groups to geometry and back. Zbl 1428.20001Climenhaga, Vaughn; Katok, Anatole 1 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 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 Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021Fayad, Bassam; Katok, Anatole 6 2014 Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003Katok, Anatole; Nitică, Viorel 25 2011 Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026Damjanovic, Danijela; Katok, Anatole 16 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 10 2011 Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017Damjanović, Danijela; Katok, Anatole 25 2010 Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037Katok, Anatole; Hertz, Federico Rodriguez 6 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 36 2007 Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017Kalinin, Boris; Katok, Anatole 10 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 69 2006 Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304Katok, Anatole; Thouvenot, Jean-Paul 22 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 16 2005 Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029Damjanović, Danijela; Katok, Anatole 14 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 51 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 73 2003 Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001Katok, Anatole 43 2003 Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023Einsiedler, Manfred; Katok, Anatole 18 2003 Handbook of dynamical systems. Volume 1A. Zbl 1013.00016 32 2002 Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005Katok, Anatole; Katok, Svetlana; Schmidt, Klaus 22 2002 Principal structures. Zbl 1047.37001Hasselblatt, Boris; Katok, Anatole 16 2002 Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029Feres, Renato; Katok, Anatole 9 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. 28 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 99 1997 Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009Katok, Anatole; Thouvenot, Jean-Paul 41 1997 Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010Katok, A.; Spatzier, R. J. 40 1997 Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021Katok, A.; Spatzier, R. J. 46 1996 Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082Katok, A.; Kononenko, A. 27 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 1,177 1995 Caustics for inner and outer billiards. Zbl 0839.58036Gutkin, Eugene; Katok, Anatole 28 1995 Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039Katok, Anatole; Katok, Svetlana 14 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. 52 1994 Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029Katok, Anatole; Burns, Keith 36 1994 Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026Katok, A.; Spatzier, R. J. 22 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. 31 1991 Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041Katok, Anatole; Knieper, Gerhard; Weiss, Howard 17 1991 Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034Hurder, S.; Katok, A. 54 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. 7 1990 Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H. 40 1989 Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050Feres, Renato; Katok, Anatoly 8 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 32 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 78 1986 Random perturbations of transformations of an interval. Zbl 0616.60064Katok, A.; Kifer, Y. 15 1986 Manifolds with non-positive curvature. Zbl 0572.58019Burns, K.; Katok, A. 33 1985 Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015Hurder, S.; Katok, A. 5 1984 Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016Katok, Anatole 4 1984 On local entropy. Zbl 0533.58020Brin, M.; Katok, A. 83 1983 Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032Katok, A. 9 1983 Entropy and closed geodesics. Zbl 0525.58027Katok, A. 48 1982 Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048Katok, A. 33 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. 12 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. 387 1980 Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009Katok, Anatole 46 1980 Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016Katok, A. 12 1980 ...and 22 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,463 Authors 35 Katok, Anatole 23 Pesin, Yakov Borisovich 21 Barreira, Luis Manuel 21 de la Llave, Rafael 21 Einsiedler, Manfred Leopold 19 Lindenstrauss, Elon 19 Morales, Carlos Arnoldo 19 Sun, Wenxiang 19 Varandas, Paulo 17 Pollicott, Mark 17 Rodriguez-Hertz, Federico 16 Fayad, Bassam R. 16 Kuznetsov, Sergey P. 16 Mesón, Alejandro M. 16 Troubetzkoy, Serge Eugene 16 Valls Anglés, Cláudia 16 Vericat, Fernando 15 Gelfert, Katrin Grit 15 Huang, Wen 15 Oertel-Jäger, Tobias Hendrik 15 Kanigowski, Adam 15 Lemańczyk, Mariusz 15 Paternain, Gabriel Pedro 15 Young, Lai-Sang 15 Zhao, Yun 14 Chen, Ercai 14 Forni, Giovanni 14 Gutkin, Eugene 14 Hasselblatt, Boris 14 Kalinin, Boris 14 Sadovskaya, Victoria 13 Climenhaga, Vaughn 13 Damjanović, Danijela 13 Frączek, Krzysztof Marek 13 Ledrappier, François 13 Mihailescu, Eugen Gh. 13 Ryzhikov, Valeriĭ Valentinovich 13 Spatzier, Ralf J. 13 Yang, Jiagang 12 Buzzi, Jérôme 12 Cao, Yongluo 12 Chaika, Jonathan 12 Crovisier, Sylvain 12 Dolgopyat, Dmitry 11 Avila Cordeiro de Melo, Artur 11 Bunimovich, Leonid Abramovich 11 Dragičević, Davor 11 Duan, Huagui 11 Ferenczi, Sébastien 11 Knieper, Gerhard 11 Kolesov, Andreĭ Yur’evich 11 Kunde, Philipp 11 Stoyanov, Luchezar N. 11 Wilkinson, Amie 11 Ye, Xiangdong 10 Baladi, Viviane 10 Bonatti, Christian 10 Glyzin, Sergeĭ D. 10 Long, Yiming 10 Tian, Xueting 10 Tien Cuong Dinh 10 Weiss, Howard 10 Zhou, Yunhua 9 Chernov, Nikolai Ivanovich 9 Guillarmou, Colin 9 Hurder, Steven E. 9 Kawan, Christoph 9 Llibre, Jaume 9 Masur, Howard A. 9 Rozov, Nikolaĭ Khristovich 9 Sibony, Nessim 8 Andres, Jan 8 Araújo, Vítor 8 Backes, Lucas H. 8 Bessa, Mário 8 Biś, Andrzej 8 Burns, Keith 8 Cheng, Wenchiao 8 de Thélin, Henry 8 Gerber, Marlies 8 Giona, Massimiliano 8 Gogolev, Andrey 8 Gorodetskii, Anton Semenovich 8 Hubert, Pascal 8 Labourie, François 8 Le Calvez, Patrice 8 Liang, Chao 8 Liao, Gang 8 Potrie, Rafael 8 Rodriguez Hertz, Jana 8 Shu, Lin 8 Tahzibi, Ali 8 Thompson, Daniel J. 8 Ulcigrai, Corinna 8 Vetokhin, Alexandr N. 8 Viana, Marcelo 8 Wang, Wei 8 Wang, Zhenqi Jenny 8 Wolf, Christian K. 8 Zhu, Yujun ...and 2,363 more Authors all top 5 Cited in 356 Serials 248 Ergodic Theory and Dynamical Systems 105 Communications in Mathematical Physics 95 Israel Journal of Mathematics 94 Discrete and Continuous Dynamical Systems 90 Transactions of the American Mathematical Society 85 Proceedings of the American Mathematical Society 75 Journal of Statistical Physics 68 Journal of Differential Equations 59 Inventiones Mathematicae 57 Physica D 53 Advances in Mathematics 47 Annales de l’Institut Fourier 44 Journal of Modern Dynamics 42 Duke Mathematical Journal 39 Dynamical Systems 36 Journal of Mathematical Analysis and Applications 31 Mathematische Zeitschrift 29 Journal d’Analyse Mathématique 29 Mathematische Annalen 29 Journal of Dynamics and Differential Equations 29 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 29 Annals of Mathematics. Second Series 28 Nonlinearity 27 Mathematical Notes 27 Topology and its Applications 25 Chaos, Solitons and Fractals 24 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 21 Functional Analysis and its Applications 20 Journal of Functional Analysis 20 Qualitative Theory of Dynamical Systems 20 Proceedings of the Steklov Institute of Mathematics 19 Journal of the American Mathematical Society 19 Geometry & Topology 19 Journal of the European Mathematical Society (JEMS) 19 Acta Mathematica Sinica. English Series 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 16 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 15 Commentarii Mathematici Helvetici 15 Monatshefte für Mathematik 15 Journal of Dynamical and Control Systems 14 Annales Henri Poincaré 14 Bulletin of the Brazilian Mathematical Society. New Series 13 Stochastics and Dynamics 12 Journal of Difference Equations and Applications 12 SIAM Journal on Applied Dynamical Systems 12 Science China. Mathematics 11 Physics Letters. A 11 Publications Mathématiques 10 Mathematical Proceedings of the Cambridge Philosophical Society 10 Journal of Geometry and Physics 10 Journal of Nonlinear Science 10 Electronic Research Announcements of the American Mathematical Society 9 The Journal of Geometric Analysis 9 Calculus of Variations and Partial Differential Equations 9 Differential Equations 9 Discrete and Continuous Dynamical Systems. Series B 9 Journal of Fixed Point Theory and Applications 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 Bulletin de la Société Mathématique de France 7 Differential Geometry and its Applications 7 Journal of Topology and Analysis 6 Automatica 6 Annales de l’Institut Henri Poincaré. Physique Théorique 6 Experimental Mathematics 6 Communications in Nonlinear Science and Numerical Simulation 6 Journal de l’École Polytechnique – Mathématiques 6 Russian Journal of Nonlinear Dynamics 5 Journal of Mathematical Biology 5 Acta Mathematica 5 Memoirs of the American Mathematical Society 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 Algebraic & Geometric Topology 5 Entropy 5 Discrete and Continuous Dynamical Systems. Series S 4 Journal of Computational Physics 4 Moscow University Mathematics Bulletin 4 Rocky Mountain Journal of Mathematics 4 Applied Mathematics and Computation 4 Archiv der Mathematik 4 Fundamenta Mathematicae 4 Indiana University Mathematics Journal 4 Journal of Algebra ...and 256 more Serials all top 5 Cited in 63 Fields 2,265 Dynamical systems and ergodic theory (37-XX) 303 Differential geometry (53-XX) 288 Measure and integration (28-XX) 160 Ordinary differential equations (34-XX) 146 Manifolds and cell complexes (57-XX) 141 Global analysis, analysis on manifolds (58-XX) 132 General topology (54-XX) 113 Topological groups, Lie groups (22-XX) 107 Number theory (11-XX) 103 Probability theory and stochastic processes (60-XX) 96 Several complex variables and analytic spaces (32-XX) 94 Mechanics of particles and systems (70-XX) 79 Partial differential equations (35-XX) 74 Statistical mechanics, structure of matter (82-XX) 67 Operator theory (47-XX) 58 Group theory and generalizations (20-XX) 51 Functions of a complex variable (30-XX) 48 Quantum theory (81-XX) 47 Systems theory; control (93-XX) 43 Computer science (68-XX) 32 Functional analysis (46-XX) 32 Numerical analysis (65-XX) 32 Biology and other natural sciences (92-XX) 32 Information and communication theory, circuits (94-XX) 31 Fluid mechanics (76-XX) 25 Algebraic geometry (14-XX) 23 Combinatorics (05-XX) 21 Difference and functional equations (39-XX) 21 Convex and discrete geometry (52-XX) 18 Real functions (26-XX) 17 Algebraic topology (55-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 16 Abstract harmonic analysis (43-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Geometry (51-XX) 14 Statistics (62-XX) 10 History and biography (01-XX) 9 Mathematical logic and foundations (03-XX) 8 General and overarching topics; collections (00-XX) 8 \(K\)-theory (19-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Optics, electromagnetic theory (78-XX) 8 Geophysics (86-XX) 7 Operations research, mathematical programming (90-XX) 6 Associative rings and algebras (16-XX) 6 Potential theory (31-XX) 6 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Category theory; homological algebra (18-XX) 4 Special functions (33-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Commutative algebra (13-XX) 3 Nonassociative rings and algebras (17-XX) 2 General algebraic systems (08-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Relativity and gravitational theory (83-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Astronomy and astrophysics (85-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. Updates and corrections should be made in Wikidata.