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Katok, Anatole B.

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Author ID: katok.anatole-b Recent zbMATH articles by "Katok, Anatole B."
Published as: Katok, A.; Katok, A. B.; Katok, Anatole; Katok, Anatole B.; Katok, Anatoly
External Links: MGP · Math-Net.Ru · Wikidata · GND
Documents Indexed: 133 Publications since 1964, including 16 Books
Biographic References: 6 Publications
all top 5

Co-Authors

35 single-authored
10 Rodriguez-Hertz, Federico
7 Hasselblatt, Boris
6 Damjanović, Danijela
6 Kalinin, Boris
6 Stepin, Anatolii Mikhailovich
5 Anosov, Dmitriĭ Viktorovich
5 Katok, Svetlana R.
5 Spatzier, Ralf J.
4 Weiss, Howard
4 Zemlyakov, A. N.
3 Einsiedler, Manfred Leopold
3 Fayad, Bassam R.
3 Feres, Renato
3 Hurder, Steven E.
3 Knieper, Gerhard
3 Lewis, James Welsh
3 Niţică, Viorel
3 Pesin, Yakov Borisovich
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 Neĭshtadt, Anatoliĭ Iserovich
2 Pollicott, Mark
2 Schmidt, Klaus
2 Thouvenot, Jean-Paul
1 Afraimovich, Valentin S.
1 Aseev, Sergei M.
1 Bernstein, David
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 Gerber, Marlies
1 Gonchenko, Sergey V.
1 Grigorchuk, Rostislav Ivanovich
1 Gunesch, Roland
1 Gurevich, B. M.
1 Guysinsky, Moisey
1 Ilyashenko, Yulij Sergeevich
1 Kashchenko, Sergeĭ Aleksandrovich
1 Kifer, Yuri
1 Klimenko, Alexey V.
1 Kononenko, Alexey
1 Kulikov, M. S.
1 Leksin, Vladimir Pavlovich
1 Lemańczyk, Mariusz
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 Przytycki, Feliks
1 Robinson, E. Arthur jun.
1 Samoĭlenko, Anatoliĭ Mykhaĭlovych
1 Sataev, A. B.
1 Sataev, Evgueni A.
1 Sharkovskiĭ, Oleksandr Mykolaiovych
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

16 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

Publications by Year

Citations contained in zbMATH Open

118 Publications have been cited 3,523 times in 2,572 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.
350
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
92
1997
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
85
1986
On local entropy. Zbl 0533.58020
Brin, M.; Katok, A.
82
1983
Approximations in ergodic theory. Zbl 0172.07202
Katok, A. B.; Stepin, A. M.
72
1967
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001
Hasselblatt, Boris; Katok, Anatole
64
2003
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004
Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
63
2006
Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021
Katok, A.
55
1979
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034
Hurder, S.; Katok, A.
48
1990
Constructions in elliptic dynamics. Zbl 1089.37012
Fayad, Bassam; Katok, Anatole
47
2004
Ergodic perturbations of degenerate integrable Hamiltonian systems. Zbl 0316.58010
Katok, A. B.
46
1974
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027
Katok, Anatole; Spatzier, Ralf J.
45
1994
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009
Katok, Anatole
43
1980
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021
Katok, A.; Spatzier, R. J.
41
1996
Entropy and closed geodesics. Zbl 0525.58027
Katok, A.
39
1982
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001
Katok, Anatole
37
2003
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
36
1989
New examples in smooth ergodic theory. Ergodic diffeomorphisms. Zbl 0255.58007
Anosov, D. V.; Katok, A. B.
36
1972
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010
Katok, A.; Spatzier, R. J.
34
1997
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009
Katok, Anatole; Thouvenot, Jean-Paul
34
1997
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042
Katok, Anatole
33
1988
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001
Katok, Anatole
32
2007
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029
Katok, Anatole; Burns, Keith
32
1994
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012
Katok, A.; Lewis, J.
31
1991
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048
Katok, A.
31
1982
Invariant measures of flows on oriented surfaces. Zbl 0298.28013
Katok, A. B.
30
1973
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040
Bernstein, David; Katok, Anatole
29
1987
Topological transitivity of billiards in polygons. Zbl 0323.58012
Zemlyakov, A. N.; Katok, A. B.
29
1976
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016
Hasselblatt, B. (ed.); Katok, A. (ed.)
28
2002
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003
Katok, Anatole; Robinson, E. A. jun.
27
2001
Neue Beispiele in der differenzierbaren Ergodentheorie. Ergodische Diffeomorphismen. Zbl 0218.58008
Anosov, D. V.; Katok, A. B.
27
1970
Manifolds with non-positive curvature. Zbl 0572.58019
Burns, K.; Katok, A.
26
1985
Caustics for inner and outer billiards. Zbl 0839.58036
Gutkin, Eugene; Katok, Anatole
25
1995
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082
Katok, A.; Kononenko, A.
24
1996
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020
Katok, A.
24
1987
Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017
Damjanović, Danijela; Katok, Anatole
21
2010
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016
Kalinin, Boris; Katok, Anatole
21
2001
Topologische Transitivität von Billards in Polygonen. Zbl 0315.58014
Zemlyakov, A. N.; Katok, A. B.
21
1975
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026
Katok, A.; Spatzier, R. J.
20
1994
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003
Katok, Anatole; Nitică, Viorel
19
2011
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304
Katok, Anatole; Thouvenot, Jean-Paul
19
2006
Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005
Katok, Anatole; Katok, Svetlana; Schmidt, Klaus
19
2002
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063
Guysinsky, M.; Katok, A.
19
1998
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038
Katok, A.; Lewis, J.
18
1996
Theory of dynamical systems and general transformation groups with invariant measure. Zbl 0399.28011
Katok, A. B.; Sinai, Ya. G.; Stepin, A. M.
18
1975
Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023
Einsiedler, Manfred; Katok, Anatole
16
2003
Ergodic theory and Weil measures for foliations. Zbl 0645.57021
Hurder, S.; Katok, A.
16
1987
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026
Damjanovic, Danijela; Katok, Anatole
15
2011
Random perturbations of transformations of an interval. Zbl 0616.60064
Katok, A.; Kifer, Y.
14
1986
Nonuniform measure rigidity. Zbl 1368.37031
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
13
2011
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017
Einsiedler, Manfred; Katok, Anatole
13
2005
Principal structures. Zbl 1047.37001
Hasselblatt, Boris; Katok, Anatole
13
2002
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037
Katok, A.; Lewis, J.; Zimmer, R.
13
1996
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039
Katok, Anatole; Katok, Svetlana
13
1995
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041
Katok, Anatole; Knieper, Gerhard; Weiss, Howard
13
1991
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029
Damjanović, Danijela; Katok, Anatole
12
2005
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032
Katok, A.
11
1983
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021
Brin, M. I.; Feldman, J.; Katok, A.
11
1981
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005
Katok, A.; Lemańczyk, M.
10
2009
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042
Katok, Anatole; Niţică, Viorel; Török, Andrei
10
2000
Monotone equivalence in ergodic theory. Zbl 0379.28008
Katok, A. B.
10
1977
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017
Kalinin, Boris; Katok, Anatole
9
2007
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029
Gerber, Marlies; Katok, Anatole
9
1982
Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016
Katok, A.
9
1980
Approximation of ergodic dynamical systems by periodic transformations. Zbl 0186.46701
Katok, A. B.; Stepin, A. M.
9
1966
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
8
2011
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023
Katok, Anatole; Katok, Svetlana
8
2005
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.
8
2000
Metric properties of measure preserving homeomorphisms. Zbl 0209.27803
Katok, A. B.; Stepin, A. M.
8
1970
Metric properties of homeomorphisms which preserve the measure. Zbl 0198.55701
Katok, A. B.; Stepin, A. M.
8
1970
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005
Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico
7
2014
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001
Katok, Anatole; Climenhaga, Vaughn
7
2008
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024
Katok, A.
7
1992
Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039
Feres, Renato; Katok, Anatole
7
1990
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050
Feres, Renato; Katok, Anatoly
7
1989
The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015
Katok, Anatole B.; Schmidt, Klaus
6
1995
Time change, monotone equivalent and standard dynamical systems. Zbl 0326.28025
Katok, A. B.
6
1975
Spectral properties of dynamical systems with an integral invariant on the torus. Zbl 0172.12102
Katok, A. B.
6
1967
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
Fayad, Bassam; Katok, Anatole
5
2014
Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029
Feres, Renato; Katok, Anatole
5
2002
Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
5
2001
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016
Katok, Anatole
5
1984
Dynamical systems with hyperbolic structure. Zbl 0598.58031
Katok, A. B.
5
1981
Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020
Katok, A. B.
5
1977
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048
Katok, Anatole; Rodriguez Hertz, Federico
4
2016
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037
Katok, Anatole; Hertz, Federico Rodriguez
4
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
4
2010
Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data. Zbl 1136.37016
Katok, Anatole; Rodriguez Hertz, Federico
4
2007
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006
Hasselblatt, B. (ed.); Katok, A. (ed.)
4
2006
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015
Damjanović, Danijela; Katok, Anatole
4
2004
Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029
Kalinin, Boris; Katok, Anatole
4
2002
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002
Katok, Anatole
4
1996
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033
Flaminio, L.; Katok, A.
4
1992
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
4
1990
A conjecture about entropy. Zbl 0628.58026
Katok, A. B.
4
1977
Standardness of automorphisms of transposition of intervals and fluxes on surfaces. Zbl 0368.58010
Katok, A. B.; Sataev, A. B.
4
1976
New progress in nonuniform measure and cocycle rigidity. Zbl 1159.37316
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
3
2008
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017
Katok, A.; Niţică, V.
3
2007
Billiard table as a playground for a mathematician. Zbl 1147.37329
Katok, A. B.
3
2005
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083
Erchenko, Alena; Katok, Anatole
1
2019
Dmitry Viktorovich Anosov: his life and mathematics. Zbl 1386.01011
Katok, Anatole
1
2017
Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002
Katok, Anatole (ed.); Pesin, Yakov (ed.); Rodriguez Hertz, Federico (ed.)
1
2017
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048
Katok, Anatole; Rodriguez Hertz, Federico
4
2016
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005
Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico
7
2014
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
Fayad, Bassam; Katok, Anatole
5
2014
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003
Katok, Anatole; Nitică, Viorel
19
2011
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026
Damjanovic, Danijela; Katok, Anatole
15
2011
Nonuniform measure rigidity. Zbl 1368.37031
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
13
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
8
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
21
2010
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037
Katok, Anatole; Hertz, Federico Rodriguez
4
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
4
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
2
2010
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005
Katok, A.; Lemańczyk, M.
10
2009
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001
Katok, Anatole; Climenhaga, Vaughn
7
2008
New progress in nonuniform measure and cocycle rigidity. Zbl 1159.37316
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
3
2008
Moscow dynamics seminars of the nineteen seventies and the early career of Yasha Pesin. Zbl 1152.01009
Katok, Anatole
2
2008
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001
Katok, Anatole
32
2007
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017
Kalinin, Boris; Katok, Anatole
9
2007
Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data. Zbl 1136.37016
Katok, Anatole; Rodriguez Hertz, Federico
4
2007
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017
Katok, A.; Niţică, V.
3
2007
Local rigidity of restrictions of Weyl chamber flows. Zbl 1113.37015
Damjanović, Danijela; Katok, Anatole
2
2007
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004
Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
63
2006
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304
Katok, Anatole; Thouvenot, Jean-Paul
19
2006
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006
Hasselblatt, B. (ed.); Katok, A. (ed.)
4
2006
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017
Einsiedler, Manfred; Katok, Anatole
13
2005
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029
Damjanović, Danijela; Katok, Anatole
12
2005
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023
Katok, Anatole; Katok, Svetlana
8
2005
Billiard table as a playground for a mathematician. Zbl 1147.37329
Katok, A. B.
3
2005
Constructions in elliptic dynamics. Zbl 1089.37012
Fayad, Bassam; Katok, Anatole
47
2004
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015
Damjanović, Danijela; Katok, Anatole
4
2004
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001
Hasselblatt, Boris; Katok, Anatole
64
2003
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001
Katok, Anatole
37
2003
Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023
Einsiedler, Manfred; Katok, Anatole
16
2003
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016
Hasselblatt, B. (ed.); Katok, A. (ed.)
28
2002
Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005
Katok, Anatole; Katok, Svetlana; Schmidt, Klaus
19
2002
Principal structures. Zbl 1047.37001
Hasselblatt, Boris; Katok, Anatole
13
2002
Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029
Feres, Renato; Katok, Anatole
5
2002
Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029
Kalinin, Boris; Katok, Anatole
4
2002
The development of dynamics in the 20th century and the contribution of Jürgen Moser. Zbl 1018.37001
Hasselblatt, Boris; Katok, Anatole
2
2002
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003
Katok, Anatole; Robinson, E. A. jun.
27
2001
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016
Kalinin, Boris; Katok, Anatole
21
2001
Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
5
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
Katok, Anatole (ed.); de la Llave, Rafael (ed.); Pesin, Yakov (ed.); Weiss, Howard (ed.)
2
2001
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042
Katok, Anatole; Niţică, Viorel; Török, Andrei
10
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.
8
2000
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063
Guysinsky, M.; Katok, A.
19
1998
Entropy and growth of expanding periodic orbits for one-dimensional maps. Zbl 0915.58025
Katok, A.; Mezhirov, A.
1
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
92
1997
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010
Katok, A.; Spatzier, R. J.
34
1997
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009
Katok, Anatole; Thouvenot, Jean-Paul
34
1997
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021
Katok, A.; Spatzier, R. J.
41
1996
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082
Katok, A.; Kononenko, A.
24
1996
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038
Katok, A.; Lewis, J.
18
1996
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037
Katok, A.; Lewis, J.; Zimmer, R.
13
1996
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002
Katok, Anatole
4
1996
Nonstationary normal forms and rigidity of group actions. Zbl 0871.58073
Katok, A.; Spatzier, R. J.
2
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
25
1995
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039
Katok, Anatole; Katok, Svetlana
13
1995
The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015
Katok, Anatole B.; Schmidt, Klaus
6
1995
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027
Katok, Anatole; Spatzier, Ralf J.
45
1994
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029
Katok, Anatole; Burns, Keith
32
1994
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026
Katok, A.; Spatzier, R. J.
20
1994
Women in Soviet mathematics. Zbl 1194.01176
Katok, Anatole; Katok, Svetlana
1
1993
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024
Katok, A.
7
1992
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033
Flaminio, L.; Katok, A.
4
1992
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012
Katok, A.; Lewis, J.
31
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
13
1991
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034
Hurder, S.; Katok, A.
48
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
7
1990
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
4
1990
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
36
1989
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050
Feres, Renato; Katok, Anatoly
7
1989
Vladimir Abramovich Rokhlin (23 August 1919 to 3 December 1984): Introductory note. Zbl 0688.01012
Katok, A.
1
1989
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042
Katok, Anatole
33
1988
Weakly mixing billiards. Zbl 0673.58028
Gutkin, E.; Katok, A.
2
1988
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040
Bernstein, David; Katok, Anatole
29
1987
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020
Katok, A.
24
1987
Ergodic theory and Weil measures for foliations. Zbl 0645.57021
Hurder, S.; Katok, A.
16
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
85
1986
Random perturbations of transformations of an interval. Zbl 0616.60064
Katok, A.; Kifer, Y.
14
1986
Manifolds with non-positive curvature. Zbl 0572.58019
Burns, K.; Katok, A.
26
1985
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016
Katok, Anatole
5
1984
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015
Hurder, S.; Katok, A.
3
1984
On local entropy. Zbl 0533.58020
Brin, M.; Katok, A.
82
1983
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032
Katok, A.
11
1983
Entropy and closed geodesics. Zbl 0525.58027
Katok, A.
39
1982
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048
Katok, A.
31
1982
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029
Gerber, Marlies; Katok, Anatole
9
1982
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021
Brin, M. I.; Feldman, J.; Katok, A.
11
1981
Dynamical systems with hyperbolic structure. Zbl 0598.58031
Katok, A. B.
5
1981
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015
Katok, A.
350
1980
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009
Katok, Anatole
43
1980
Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016
Katok, A.
9
1980
Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021
Katok, A.
55
1979
The special representation theorem for multi-dimensional group actions. Zbl 0388.28024
Katok, A. B.
3
1978
Monotone equivalence in ergodic theory. Zbl 0379.28008
Katok, A. B.
10
1977
Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020
Katok, A. B.
5
1977
...and 18 more Documents
all top 5

Cited by 2,419 Authors

33 Katok, Anatole B.
22 de la Llave, Rafael
21 Morales, Carlos Arnoldo
21 Pesin, Yakov Borisovich
20 Barreira, Luis Manuel
20 Einsiedler, Manfred Leopold
19 Sun, Wenxiang
18 Lindenstrauss, Elon
17 Kuznetsov, Sergey P.
17 Troubetzkoy, Serge Eugene
17 Varandas, Paulo
16 Pollicott, Mark
15 Huang, Wen
15 Oertel-Jäger, Tobias Hendrik
15 Lemańczyk, Mariusz
15 Valls Anglés, Cláudia
14 Fayad, Bassam R.
14 Gelfert, Katrin Grit
14 Gutkin, Eugene
14 Kalinin, Boris
14 Mesón, Alejandro M.
14 Paternain, Gabriel Pedro
14 Rodriguez-Hertz, Federico
14 Vericat, Fernando
14 Young, Lai-Sang
13 Chen, Ercai
13 Sadovskaya, Victoria
12 Cao, Yongluo
12 Ledrappier, François
12 Mihailescu, Eugen Gh.
12 Ryzhikov, Valeriĭ Valentinovich
12 Spatzier, Ralf J.
12 Yang, Jiagang
12 Zhao, Yun
11 Bunimovich, Leonid Abramovich
11 Buzzi, Jérôme
11 Chaika, Jonathan
11 Climenhaga, Vaughn
11 Crovisier, Sylvain
11 Ferenczi, Sébastien
11 Frączek, Krzysztof Marek
11 Ye, Xiangdong
10 Avila Cordeiro de Melo, Artur
10 Damjanović, Danijela
10 Duan, Huagui
10 Forni, Giovanni
10 Hasselblatt, Boris
10 Kanigowski, Adam
10 Knieper, Gerhard
10 Liao, Gang
10 Long, Yiming
10 Tian, Xueting
10 Tien Cuong Dinh
10 Weiss, Howard
10 Zhou, Yunhua
9 Bonatti, Christian
9 Chernov, Nikolai Ivanovich
9 Dolgopyat, Dmitry
9 Hurder, Steven E.
9 Kawan, Christoph
9 Kunde, Philipp
9 Llibre, Jaume
9 Masur, Howard A.
9 Qin, Wenxin
9 Sibony, Nessim
9 Stoyanov, Luchezar N.
9 Wilkinson, Amie
8 Arbieto, Alexander
8 Baladi, Viviane
8 Bessa, Mário
8 de Thélin, Henry
8 Dragičević, Davor
8 Giona, Massimiliano
8 Hubert, Pascal
8 Kolesov, Andreĭ Yur’evich
8 Labourie, François
8 Liang, Chao
8 Rozov, Nikolaĭ Khristovich
8 Ulcigrai, Corinna
8 Wang, Wei
8 Wang, Zhenqi Jenny
8 Zhu, Yujun
7 Alpern, Steve
7 Araújo, Vítor
7 Backes, Lucas H.
7 Benoist, Yves
7 Boyland, Philip L.
7 Burns, Keith
7 Cheng, Wenchiao
7 Del Magno, Gianluigi
7 Fang, Yong
7 Gerber, Marlies
7 Glyzin, Sergeĭ D.
7 Gogolev, Andrey
7 Guillarmou, Colin
7 Kifer, Yuri
7 Kocsard, Alejandro
7 Kułaga-Przymus, Joanna
7 Liverani, Carlangelo
7 Potrie, Rafael
...and 2,319 more Authors
all top 5

Cited in 339 Serials

210 Ergodic Theory and Dynamical Systems
103 Communications in Mathematical Physics
92 Israel Journal of Mathematics
88 Discrete and Continuous Dynamical Systems
86 Transactions of the American Mathematical Society
85 Proceedings of the American Mathematical Society
70 Journal of Statistical Physics
68 Journal of Differential Equations
66 Physica D
56 Inventiones Mathematicae
49 Advances in Mathematics
46 Annales de l’Institut Fourier
42 Journal of Modern Dynamics
39 Duke Mathematical Journal
34 Journal of Mathematical Analysis and Applications
30 Dynamical Systems
28 Journal d’Analyse Mathématique
28 Chaos, Solitons and Fractals
28 Mathematische Zeitschrift
28 Topology and its Applications
28 Annals of Mathematics. Second Series
27 Mathematische Annalen
27 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
26 Nonlinearity
25 Mathematical Notes
24 Geometric and Functional Analysis. GAFA
23 Bulletin of the American Mathematical Society. New Series
23 Chaos
22 Geometriae Dedicata
22 Journal of Mathematical Sciences (New York)
21 Journal of Dynamics and Differential Equations
21 Regular and Chaotic Dynamics
20 Journal of Functional Analysis
20 Proceedings of the Steklov Institute of Mathematics
19 Functional Analysis and its Applications
19 Geometry & Topology
18 Comptes Rendus. Mathématique. Académie des Sciences, Paris
17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
17 Journal of the American Mathematical Society
17 Qualitative Theory of Dynamical Systems
16 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
16 Journal of the European Mathematical Society (JEMS)
15 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
14 Bulletin of the Brazilian Mathematical Society. New Series
13 Commentarii Mathematici Helvetici
13 Monatshefte für Mathematik
13 Acta Mathematica Sinica. English Series
13 Annales Henri Poincaré
12 Physics Letters. A
12 Journal of Dynamical and Control Systems
12 Stochastics and Dynamics
11 Publications Mathématiques
11 Journal of Difference Equations and Applications
10 Journal of Nonlinear Science
10 Electronic Research Announcements of the American Mathematical Society
10 Discrete and Continuous Dynamical Systems. Series B
10 Science China. Mathematics
9 Journal of Geometry and Physics
9 The Journal of Geometric Analysis
9 Calculus of Variations and Partial Differential Equations
8 Journal of Mathematical Physics
8 Mathematical Proceedings of the Cambridge Philosophical Society
8 Theoretical Computer Science
8 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
8 Differential Equations
8 SIAM Journal on Applied Dynamical Systems
7 Bulletin de la Société Mathématique de France
7 Compositio Mathematica
7 Communications in Nonlinear Science and Numerical Simulation
7 Journal of Topology and Analysis
6 Automatica
6 Systems & Control Letters
6 Differential Geometry and its Applications
6 Annales de l’Institut Henri Poincaré. Physique Théorique
5 Journal of Computational Physics
5 Journal of Mathematical Biology
5 Acta Mathematica
5 Memoirs of the American Mathematical Society
5 Linear Algebra and its Applications
5 Boletim da Sociedade Brasileira de Matemática. Nova Série
5 Russian Mathematics
5 Experimental Mathematics
5 Algebraic & Geometric Topology
5 Entropy
5 Journal of Dynamical Systems and Geometric Theories
5 Discrete and Continuous Dynamical Systems. Series S
5 Journal de l’École Polytechnique – Mathématiques
5 Nelineĭnaya Dinamika
4 Moscow University Mathematics Bulletin
4 Rocky Mountain Journal of Mathematics
4 Fundamenta Mathematicae
4 Journal of Algebra
4 Journal of Computational and Applied Mathematics
4 Michigan Mathematical Journal
4 Annals of Global Analysis and Geometry
4 Probability Theory and Related Fields
4 St. Petersburg Mathematical Journal
4 Mathematical Physics, Analysis and Geometry
4 Conformal Geometry and Dynamics
4 Journal of the Institute of Mathematics of Jussieu
...and 239 more Serials
all top 5

Cited in 62 Fields

2,077 Dynamical systems and ergodic theory (37-XX)
280 Differential geometry (53-XX)
266 Measure and integration (28-XX)
149 Ordinary differential equations (34-XX)
133 Manifolds and cell complexes (57-XX)
132 Global analysis, analysis on manifolds (58-XX)
129 General topology (54-XX)
105 Topological groups, Lie groups (22-XX)
97 Number theory (11-XX)
95 Probability theory and stochastic processes (60-XX)
94 Mechanics of particles and systems (70-XX)
90 Several complex variables and analytic spaces (32-XX)
72 Partial differential equations (35-XX)
72 Statistical mechanics, structure of matter (82-XX)
60 Operator theory (47-XX)
53 Group theory and generalizations (20-XX)
50 Quantum theory (81-XX)
48 Systems theory; control (93-XX)
45 Functions of a complex variable (30-XX)
41 Computer science (68-XX)
32 Numerical analysis (65-XX)
31 Functional analysis (46-XX)
31 Biology and other natural sciences (92-XX)
31 Information and communication theory, circuits (94-XX)
29 Fluid mechanics (76-XX)
23 Combinatorics (05-XX)
22 Algebraic geometry (14-XX)
20 Difference and functional equations (39-XX)
19 Convex and discrete geometry (52-XX)
17 Real functions (26-XX)
17 Calculus of variations and optimal control; optimization (49-XX)
17 Algebraic topology (55-XX)
16 Abstract harmonic analysis (43-XX)
16 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
13 Geometry (51-XX)
12 Linear and multilinear algebra; matrix theory (15-XX)
12 Statistics (62-XX)
9 History and biography (01-XX)
8 Mathematical logic and foundations (03-XX)
8 Harmonic analysis on Euclidean spaces (42-XX)
8 Optics, electromagnetic theory (78-XX)
8 Operations research, mathematical programming (90-XX)
7 General and overarching topics; collections (00-XX)
7 \(K\)-theory (19-XX)
7 Geophysics (86-XX)
6 Associative rings and algebras (16-XX)
6 Mechanics of deformable solids (74-XX)
5 Special functions (33-XX)
5 Classical thermodynamics, heat transfer (80-XX)
4 Potential theory (31-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
2 General algebraic systems (08-XX)
2 Commutative algebra (13-XX)
2 Category theory; homological algebra (18-XX)
2 Integral transforms, operational calculus (44-XX)
2 Relativity and gravitational theory (83-XX)
1 Field theory and polynomials (12-XX)
1 Nonassociative rings and algebras (17-XX)
1 Sequences, series, summability (40-XX)
1 Integral equations (45-XX)
1 Astronomy and astrophysics (85-XX)
1 Mathematics education (97-XX)

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