## Katok, Anatole

Compute Distance To:
 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
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### 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.
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### 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
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### 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)

### 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 0878.58020
Katok, Anatole; Hasselblatt, Boris
1995
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015
Katok, A.
1980
Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019
Katok, Anatole; Hasselblatt, Boris
1997
On local entropy. Zbl 0533.58020
Brin, M.; Katok, A.
1983
Approximations in ergodic theory. Zbl 0172.07202
Katok, A. B.; Stepin, A. M.
1967
Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001
Katok, Anatole; Strelcyn, Jean-Marie
1986
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001
Hasselblatt, Boris; Katok, Anatole
2003
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004
Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
2006
Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021
Katok, A.
1979
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034
Hurder, S.; Katok, A.
1990
Constructions in elliptic dynamics. Zbl 1089.37012
2004
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027
Katok, Anatole; Spatzier, Ralf J.
1994
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021
Katok, A.; Spatzier, R. J.
1996
Ergodic perturbations of degenerate integrable Hamiltonian systems. Zbl 0316.58010
Katok, A. B.
1974
Entropy and closed geodesics. Zbl 0525.58027
Katok, A.
1982
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009
Katok, Anatole
1980
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001
Katok, Anatole
2003
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010
Katok, A.; Spatzier, R. J.
1997
New examples in smooth ergodic theory. Ergodic diffeomorphisms. Zbl 0255.58007
Anosov, D. V.; Katok, A. B.
1972
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
1989
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009
Katok, Anatole; Thouvenot, Jean-Paul
1997
Topological transitivity of billiards in polygons. Zbl 0323.58012
Zemlyakov, A. N.; Katok, A. B.
1976
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029
Katok, Anatole; Burns, Keith
1994
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001
Katok, Anatole
2007
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048
Katok, A.
1982
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042
Katok, Anatole
1988
Manifolds with non-positive curvature. Zbl 0572.58019
Burns, K.; Katok, A.
1985
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016
2002
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040
Bernstein, David; Katok, Anatole
1987
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012
Katok, A.; Lewis, J.
1991
Caustics for inner and outer billiards. Zbl 0839.58036
Gutkin, Eugene; Katok, Anatole
1995
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003
Katok, Anatole; Robinson, E. A. jun.
2001
Local rigidity of partially hyperbolic actions I. KAM method and $${\mathbb Z^k}$$ actions on the torus. Zbl 1209.37017
Damjanović, Danijela; Katok, Anatole
2010
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082
Katok, A.; Kononenko, A.
1996
Invariant measures of flows on oriented surfaces. Zbl 0298.28013
Katok, A. B.
1973
Neue Beispiele in der differenzierbaren Ergodentheorie. Ergodische Diffeomorphismen. Zbl 0218.58008
Anosov, D. V.; Katok, A. B.
1970
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020
Katok, A.
1987
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003
Katok, Anatole; Nitică, Viorel
2011
Rigidity of measurable structure for $$\mathbb Z^d$$-actions by automorphisms of a torus. Zbl 1035.37005
Katok, Anatole; Katok, Svetlana; Schmidt, Klaus
2002
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026
Katok, A.; Spatzier, R. J.
1994
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304
Katok, Anatole; Thouvenot, Jean-Paul
2006
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016
Kalinin, Boris; Katok, Anatole
2001
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063
Guysinsky, M.; Katok, A.
1998
Topologische Transitivität von Billards in Polygonen. Zbl 0315.58014
Zemlyakov, A. N.; Katok, A. B.
1975
Principal structures. Zbl 1047.37001
Hasselblatt, Boris; Katok, Anatole
2002
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038
Katok, A.; Lewis, J.
1996
Theory of dynamical systems and general transformation groups with invariant measure. Zbl 0399.28011
Katok, A. B.; Sinai, Ya. G.; Stepin, A. M.
1975
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041
Katok, Anatole; Knieper, Gerhard; Weiss, Howard
1991
Invariant measures on $$G/{\Gamma}$$ for split simple Lie groups $$G$$. Zbl 1022.22023
Einsiedler, Manfred; Katok, Anatole
2003
Ergodic theory and Weil measures for foliations. Zbl 0645.57021
Hurder, S.; Katok, A.
1987
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017
Einsiedler, Manfred; Katok, Anatole
2005
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026
Damjanovic, Danijela; Katok, Anatole
2011
Random perturbations of transformations of an interval. Zbl 0616.60064
Katok, A.; Kifer, Y.
1986
Monotone equivalence in ergodic theory. Zbl 0379.28008
Katok, A. B.
1977
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic $$\mathbb R^k$$ actions. Zbl 1109.37029
Damjanović, Danijela; Katok, Anatole
2005
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039
Katok, Anatole; Katok, Svetlana
1995
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037
Katok, A.; Lewis, J.; Zimmer, R.
1996
Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016
Katok, A.
1980
Nonuniform measure rigidity. Zbl 1368.37031
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
2011
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021
Brin, M. I.; Feldman, J.; Katok, A.
1981
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029
Gerber, Marlies; Katok, Anatole
1982
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042
Katok, Anatole; Niţică, Viorel; Török, Andrei
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 1291.37027
Damjanović, Danijela; Katok, Anatole
2011
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017
Kalinin, Boris; Katok, Anatole
2007
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005
Katok, A.; Lemańczyk, M.
2009
Ergodic theory and dynamics of $$G$$-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029
Feres, Renato; Katok, Anatole
2002
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032
Katok, A.
1983
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023
Katok, Anatole; Katok, Svetlana
2005
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050
Feres, Renato; Katok, Anatoly
1989
Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. With an appendix by Alex Furman. Zbl 1009.37013
Gunesch, Roland; Katok, Anatole B.
2000
Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039
Feres, Renato; Katok, Anatole
1990
Approximation of ergodic dynamical systems by periodic transformations. Zbl 0186.46701
Katok, A. B.; Stepin, A. M.
1966
Metric properties of homeomorphisms which preserve the measure. Zbl 0198.55701
Katok, A. B.; Stepin, A. M.
1970
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024
Katok, A.
1992
The cohomology of expansive $$\mathbb{Z}^ d$$-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015
Katok, Anatole B.; Schmidt, Klaus
1995
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
2014
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005
Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico
2014
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
1990
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001
Katok, Anatole; Climenhaga, Vaughn
2008
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083
Erchenko, Alena; Katok, Anatole
2019
Mixed spectrum reparameterizations of linear flows on $$\mathbb T^2$$. Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
2001
Metric properties of measure preserving homeomorphisms. Zbl 0209.27803
Katok, A. B.; Stepin, A. M.
1970
Time change, monotone equivalent and standard dynamical systems. Zbl 0326.28025
Katok, A. B.
1975
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015
Hurder, S.; Katok, A.
1984
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037
Katok, Anatole; Hertz, Federico Rodriguez
2010
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006
2006
Spectral properties of dynamical systems with an integral invariant on the torus. Zbl 0172.12102
Katok, A. B.
1967
Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020
Katok, A. B.
1977
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048
Katok, Anatole; Rodriguez Hertz, Federico
2016
Measurable rigidity and disjointness for $$\mathbb Z^ k$$ actions by toral automorphisms. Zbl 1056.37029
Kalinin, Boris; Katok, Anatole
2002
Dynamical systems with hyperbolic structure. Zbl 0598.58031
Katok, A. B.
1981
Standardness of automorphisms of transposition of intervals and fluxes on surfaces. Zbl 0368.58010
Katok, A. B.; Sataev, A. B.
1976
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015
Damjanović, Danijela; Katok, Anatole
2004
Rigidity of real-analytic actions of $$SL(n,\mathbb Z)$$ on $$\mathbb T^n$$: a case of realization of Zimmer program. Zbl 1192.37025
Katok, Anatole; Hertz, Federico Rodriguez
2010
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017
Katok, A.; Niţică, V.
2007
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002
Katok, Anatole
1996
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033
Flaminio, L.; Katok, A.
1992
Uniqueness of large invariant measures for $$\mathbb Z^k$$ actions with Cartan homotopy data. Zbl 1136.37016
Katok, Anatole; Rodriguez Hertz, Federico
2007
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016
Katok, Anatole
1984
A conjecture about entropy. Zbl 0628.58026
Katok, A. B.
1977
Flexibility of Lyapunov exponents. Zbl 1495.37024
Bochi, J.; Katok, A.; Rodriguez Hertz, F.
2022
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083
Erchenko, Alena; Katok, Anatole
2019
Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002
2017
From groups to geometry and back. Zbl 1428.20001
Climenhaga, Vaughn; Katok, Anatole
2017
Dmitry Viktorovich Anosov: his life and mathematics. Zbl 1386.01011
Katok, Anatole
2017
Non-uniform measure rigidity for $$\mathbb{Z}^k$$ actions of symplectic type. Zbl 1388.37032
Katok, Anatole; Rodriguez Hertz, Federico
2017
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048
Katok, Anatole; Rodriguez Hertz, Federico
2016
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
2014
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005
Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico
2014
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003
Katok, Anatole; Nitică, Viorel
2011
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026
Damjanovic, Danijela; Katok, Anatole
2011
Nonuniform measure rigidity. Zbl 1368.37031
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
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 1291.37027
Damjanović, Danijela; Katok, Anatole
2011
Local rigidity of partially hyperbolic actions I. KAM method and $${\mathbb Z^k}$$ actions on the torus. Zbl 1209.37017
Damjanović, Danijela; Katok, Anatole
2010
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037
Katok, Anatole; Hertz, Federico Rodriguez
2010
Rigidity of real-analytic actions of $$SL(n,\mathbb Z)$$ on $$\mathbb T^n$$: a case of realization of Zimmer program. Zbl 1192.37025
Katok, Anatole; Hertz, Federico Rodriguez
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 1192.37026
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
2010
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005
Katok, A.; Lemańczyk, M.
2009
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001
Katok, Anatole; Climenhaga, Vaughn
2008
New progress in nonuniform measure and cocycle rigidity. Zbl 1159.37316
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
2008
Moscow dynamics seminars of the nineteen seventies and the early career of Yasha Pesin. Zbl 1152.01009
Katok, Anatole
2008
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001
Katok, Anatole
2007
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017
Kalinin, Boris; Katok, Anatole
2007
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017
Katok, A.; Niţică, V.
2007
Uniqueness of large invariant measures for $$\mathbb Z^k$$ actions with Cartan homotopy data. Zbl 1136.37016
Katok, Anatole; Rodriguez Hertz, Federico
2007
Local rigidity of restrictions of Weyl chamber flows. Zbl 1113.37015
Damjanović, Danijela; Katok, Anatole
2007
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004
Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
2006
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304
Katok, Anatole; Thouvenot, Jean-Paul
2006
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006
2006
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017
Einsiedler, Manfred; Katok, Anatole
2005
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic $$\mathbb R^k$$ actions. Zbl 1109.37029
Damjanović, Danijela; Katok, Anatole
2005
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023
Katok, Anatole; Katok, Svetlana
2005
Billiard table as a playground for a mathematician. Zbl 1147.37329
Katok, A. B.
2005
Constructions in elliptic dynamics. Zbl 1089.37012
2004
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015
Damjanović, Danijela; Katok, Anatole
2004
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001
Hasselblatt, Boris; Katok, Anatole
2003
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001
Katok, Anatole
2003
Invariant measures on $$G/{\Gamma}$$ for split simple Lie groups $$G$$. Zbl 1022.22023
Einsiedler, Manfred; Katok, Anatole
2003
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016
2002
Rigidity of measurable structure for $$\mathbb Z^d$$-actions by automorphisms of a torus. Zbl 1035.37005
Katok, Anatole; Katok, Svetlana; Schmidt, Klaus
2002
Principal structures. Zbl 1047.37001
Hasselblatt, Boris; Katok, Anatole
2002
Ergodic theory and dynamics of $$G$$-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029
Feres, Renato; Katok, Anatole
2002
Measurable rigidity and disjointness for $$\mathbb Z^ k$$ actions by toral automorphisms. Zbl 1056.37029
Kalinin, Boris; Katok, Anatole
2002
The development of dynamics in the 20th century and the contribution of Jürgen Moser. Zbl 1018.37001
Hasselblatt, Boris; Katok, Anatole
2002
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003
Katok, Anatole; Robinson, E. A. jun.
2001
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016
Kalinin, Boris; Katok, Anatole
2001
Mixed spectrum reparameterizations of linear flows on $$\mathbb T^2$$. Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
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
2001
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042
Katok, Anatole; Niţică, Viorel; Török, Andrei
2000
Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. With an appendix by Alex Furman. Zbl 1009.37013
Gunesch, Roland; Katok, Anatole B.
2000
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063
Guysinsky, M.; Katok, A.
1998
Entropy and growth of expanding periodic orbits for one-dimensional maps. Zbl 0915.58025
Katok, A.; Mezhirov, A.
1998
Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019
Katok, Anatole; Hasselblatt, Boris
1997
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010
Katok, A.; Spatzier, R. J.
1997
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009
Katok, Anatole; Thouvenot, Jean-Paul
1997
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021
Katok, A.; Spatzier, R. J.
1996
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082
Katok, A.; Kononenko, A.
1996
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038
Katok, A.; Lewis, J.
1996
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037
Katok, A.; Lewis, J.; Zimmer, R.
1996
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002
Katok, Anatole
1996
Nonstationary normal forms and rigidity of group actions. Zbl 0871.58073
Katok, A.; Spatzier, R. J.
1996
Introduction to the modern theory of dynamical systems. Zbl 0878.58020
Katok, Anatole; Hasselblatt, Boris
1995
Caustics for inner and outer billiards. Zbl 0839.58036
Gutkin, Eugene; Katok, Anatole
1995
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039
Katok, Anatole; Katok, Svetlana
1995
The cohomology of expansive $$\mathbb{Z}^ d$$-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015
Katok, Anatole B.; Schmidt, Klaus
1995
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027
Katok, Anatole; Spatzier, Ralf J.
1994
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029
Katok, Anatole; Burns, Keith
1994
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026
Katok, A.; Spatzier, R. J.
1994
Women in Soviet mathematics. Zbl 1194.01176
Katok, Anatole; Katok, Svetlana
1993
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024
Katok, A.
1992
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033
Flaminio, L.; Katok, A.
1992
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012
Katok, A.; Lewis, J.
1991
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041
Katok, Anatole; Knieper, Gerhard; Weiss, Howard
1991
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034
Hurder, S.; Katok, A.
1990
Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039
Feres, Renato; Katok, Anatole
1990
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
1990
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
1989
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050
Feres, Renato; Katok, Anatoly
1989
Vladimir Abramovich Rokhlin (23 August 1919 to 3 December 1984): Introductory note. Zbl 0688.01012
Katok, A.
1989
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042
Katok, Anatole
1988
Weakly mixing billiards. Zbl 0673.58028
Gutkin, E.; Katok, A.
1988
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040
Bernstein, David; Katok, Anatole
1987
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020
Katok, A.
1987
Ergodic theory and Weil measures for foliations. Zbl 0645.57021
Hurder, S.; Katok, A.
1987
Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001
Katok, Anatole; Strelcyn, Jean-Marie
1986
Random perturbations of transformations of an interval. Zbl 0616.60064
Katok, A.; Kifer, Y.
1986
Manifolds with non-positive curvature. Zbl 0572.58019
Burns, K.; Katok, A.
1985
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015
Hurder, S.; Katok, A.
1984
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016
Katok, Anatole
1984
On local entropy. Zbl 0533.58020
Brin, M.; Katok, A.
1983
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032
Katok, A.
1983
Entropy and closed geodesics. Zbl 0525.58027
Katok, A.
1982
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048
Katok, A.
1982
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029
Gerber, Marlies; Katok, Anatole
1982
Ergodic theory and dynamical systems II. Proceedings, special year, Maryland 1979-80. Zbl 0483.00005
1982
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021
Brin, M. I.; Feldman, J.; Katok, A.
1981
Dynamical systems with hyperbolic structure. Zbl 0598.58031
Katok, A. B.
1981
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015
Katok, A.
1980
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009
Katok, Anatole
1980
Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016
Katok, A.
1980
...and 22 more Documents
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
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### 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. Mathématique. Académie des Sciences, Paris 16 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 16 Monatshefte für Mathematik 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Commentarii Mathematici Helvetici 15 Stochastics and Dynamics 14 Annales Henri Poincaré 14 Bulletin of the Brazilian Mathematical Society. New Series 13 Journal of Difference Equations and Applications 13 SIAM Journal on Applied Dynamical Systems 12 Science China. Mathematics 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Physics Letters. 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
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### 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)

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