×

Katok, Anatole (b. 1944 d. 2018)

Author ID: katok.anatole Recent zbMATH articles by "Katok, Anatole"
Published as: Katok, Anatole; Katok, A.; Katok, A. B.; Katok, Anatole B.; Katok, Anatoly
Further Spellings: Katok, Anatoliĭ Borisovich; Каток Анатолий Борисович
External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · GND · IdRef
all top 5

Co-Authors

35 single-authored
13 Rodriguez-Hertz, Federico
9 Hasselblatt, Boris
7 Katok, Svetlana R.
7 Spatzier, Ralf J.
6 Damjanović, Danijela
6 Kalinin, Boris
6 Stëpin, Anatoliĭ Mikhaĭlovich
5 Anosov, Dmitriĭ Viktorovich
5 Fayad, Bassam R.
5 Pesin, Yakov Borisovich
4 Weiss, Howard
4 Zemlyakov, A. N.
3 Climenhaga, Vaughn
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 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 Il’yashenko, Yuliĭ Sergeevich
1 Kanigowski, Adam
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 Wei, Daren
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

Publications by Year

Citations contained in zbMATH Open

124 Publications have been cited 5,043 times in 3,556 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.
467
1980
On local entropy. Zbl 0533.58020
Brin, M.; Katok, A.
164
1983
Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019
Katok, Anatole; Hasselblatt, Boris
142
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
117
1986
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001
Hasselblatt, Boris; Katok, Anatole
99
2003
Approximations in ergodic theory. Zbl 0172.07202
Katok, A. B.; Stepin, A. M.
91
1967
Ergodic perturbations of degenerate integrable Hamiltonian systems. Zbl 0316.58010
Katok, A. B.
88
1974
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004
Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
78
2006
Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021
Katok, A.
72
1979
Constructions in elliptic dynamics. Zbl 1089.37012
Fayad, Bassam; Katok, Anatole
66
2004
Entropy and closed geodesics. Zbl 0525.58027
Katok, A.
62
1982
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034
Hurder, S.; Katok, A.
62
1990
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027
Katok, Anatole; Spatzier, Ralf J.
60
1994
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021
Katok, A.; Spatzier, R. J.
57
1996
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009
Katok, Anatole
57
1980
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001
Katok, Anatole
52
2003
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009
Katok, Anatole; Thouvenot, Jean-Paul
51
1997
New examples in smooth ergodic theory. Ergodic diffeomorphisms. Zbl 0255.58007
Anosov, D. V.; Katok, A. B.
50
1972
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
49
1989
Manifolds with non-positive curvature. Zbl 0572.58019
Burns, K.; Katok, A.
49
1985
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016
49
2002
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010
Katok, A.; Spatzier, R. J.
49
1997
Topological transitivity of billiards in polygons. Zbl 0323.58012
Zemlyakov, A. N.; Katok, A. B.
47
1976
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001
Katok, Anatole
46
2007
Topologische Transitivität von Billards in Polygonen. Zbl 0315.58014
Zemlyakov, A. N.; Katok, A. B.
45
1975
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048
Katok, A.
43
1982
Neue Beispiele in der differenzierbaren Ergodentheorie. Ergodische Diffeomorphismen. Zbl 0218.58008
Anosov, D. V.; Katok, A. B.
41
1970
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042
Katok, Anatole
40
1988
Invariant measures of flows on oriented surfaces. Zbl 0298.28013
Katok, A. B.
40
1973
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040
Bernstein, David; Katok, Anatole
39
1987
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029
Katok, Anatole; Burns, Keith
38
1994
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012
Katok, A.; Lewis, J.
36
1991
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003
Katok, Anatole; Robinson, E. A. jun.
36
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
33
2010
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003
Katok, Anatole; Nitică, Viorel
33
2011
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082
Katok, A.; Kononenko, A.
32
1996
Caustics for inner and outer billiards. Zbl 0839.58036
Gutkin, Eugene; Katok, Anatole
31
1995
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020
Katok, A.
30
1987
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304
Katok, Anatole; Thouvenot, Jean-Paul
27
2006
Principal structures. Zbl 1047.37001
Hasselblatt, Boris; Katok, Anatole
26
2002
Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005
Katok, Anatole; Katok, Svetlana; Schmidt, Klaus
25
2002
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063
Guysinsky, M.; Katok, A.
25
1998
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038
Katok, A.; Lewis, J.
24
1996
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016
Kalinin, Boris; Katok, Anatole
24
2001
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026
Katok, A.; Spatzier, R. J.
23
1994
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041
Katok, Anatole; Knieper, Gerhard; Weiss, Howard
21
1991
Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023
Einsiedler, Manfred; Katok, Anatole
20
2003
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017
Einsiedler, Manfred; Katok, Anatole
19
2005
Random perturbations of transformations of an interval. Zbl 0616.60064
Katok, A.; Kifer, Y.
19
1986
Theory of dynamical systems and general transformation groups with invariant measure. Zbl 0399.28011
Katok, A. B.; Sinai, Ya. G.; Stepin, A. M.
19
1975
Monotone equivalence in ergodic theory. Zbl 0379.28008
Katok, A. B.
18
1977
Nonuniform measure rigidity. Zbl 1368.37031
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
18
2011
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037
Katok, A.; Lewis, J.; Zimmer, R.
17
1996
Ergodic theory and Weil measures for foliations. Zbl 0645.57021
Hurder, S.; Katok, A.
17
1987
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016
Katok, Anatole
17
1984
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026
Damjanovic, Danijela; Katok, Anatole
17
2011
Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016
Katok, A.
17
1980
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029
Damjanović, Danijela; Katok, Anatole
16
2005
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039
Katok, Anatole; Katok, Svetlana
15
1995
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
14
2011
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021
Brin, M. I.; Feldman, J.; Katok, A.
14
1981
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017
Kalinin, Boris; Katok, Anatole
14
2007
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029
Gerber, Marlies; Katok, Anatole
13
1982
Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020
Katok, A. B.
13
1977
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042
Katok, Anatole; Niţică, Viorel; Török, Andrei
12
2000
Approximation of ergodic dynamical systems by periodic transformations. Zbl 0186.46701
Katok, A. B.; Stepin, A. M.
12
1966
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006
12
2006
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032
Katok, A.
12
1983
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083
Erchenko, Alena; Katok, Anatole
12
2019
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023
Katok, Anatole; Katok, Svetlana
12
2005
Metric properties of measure preserving homeomorphisms. Zbl 0209.27803
Katok, A. B.; Stepin, A. M.
11
1970
Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029
Feres, Renato; Katok, Anatole
11
2002
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050
Feres, Renato; Katok, Anatoly
10
1989
Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
10
2001
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005
Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico
10
2014
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.
10
2000
Metric properties of homeomorphisms which preserve the measure. Zbl 0198.55701
Katok, A. B.; Stepin, A. M.
10
1970
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005
Katok, A.; Lemańczyk, M.
10
2009
Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039
Feres, Renato; Katok, Anatole
9
1990
Standardness of automorphisms of transposition of intervals and fluxes on surfaces. Zbl 0368.58010
Katok, A. B.; Sataev, A. B.
9
1976
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001
Katok, Anatole; Climenhaga, Vaughn
9
2008
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
Fayad, Bassam; Katok, Anatole
9
2014
The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015
Katok, Anatole B.; Schmidt, Klaus
8
1995
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
8
1990
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024
Katok, A.
8
1992
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037
Katok, Anatole; Hertz, Federico Rodriguez
8
2010
Neue Beispiele ergodischer Diffeomorphismen glatter Mannigfaltigkeiten. Zbl 0203.56502
Anosov, D. V.; Katok, A. B.
7
1970
A conjecture about entropy. Zbl 0628.58026
Katok, A. B.
7
1977
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015
Hurder, S.; Katok, A.
7
1984
Spectral properties of dynamical systems with an integral invariant on the torus. Zbl 0172.12102
Katok, A. B.
7
1967
Time change, monotone equivalent and standard dynamical systems. Zbl 0326.28025
Katok, A. B.
7
1975
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048
Katok, Anatole; Rodriguez Hertz, Federico
7
2016
Flexibility of Lyapunov exponents. Zbl 1495.37024
Bochi, J.; Katok, A.; Rodriguez Hertz, F.
7
2022
Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029
Kalinin, Boris; Katok, Anatole
6
2002
Weakly mixing billiards. Zbl 0673.58028
Gutkin, E.; Katok, A.
5
1988
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033
Flaminio, L.; Katok, A.
5
1992
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015
Damjanović, Danijela; Katok, Anatole
5
2004
Dynamical systems with hyperbolic structure. Zbl 0598.58031
Katok, A. B.
5
1981
Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002
5
2017
Flexibility of Lyapunov exponents. Zbl 1495.37024
Bochi, J.; Katok, A.; Rodriguez Hertz, F.
7
2022
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083
Erchenko, Alena; Katok, Anatole
12
2019
Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002
5
2017
From groups to geometry and back. Zbl 1428.20001
Climenhaga, Vaughn; Katok, Anatole
4
2017
Dmitry Viktorovich Anosov: his life and mathematics. Zbl 1386.01011
Katok, Anatole
2
2017
Non-uniform measure rigidity for \(\mathbb{Z}^k\) actions of symplectic type. Zbl 1388.37032
Katok, Anatole; Rodriguez Hertz, Federico
1
2017
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048
Katok, Anatole; Rodriguez Hertz, Federico
7
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
10
2014
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
Fayad, Bassam; Katok, Anatole
9
2014
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003
Katok, Anatole; Nitică, Viorel
33
2011
Nonuniform measure rigidity. Zbl 1368.37031
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
18
2011
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026
Damjanovic, Danijela; Katok, Anatole
17
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
14
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
33
2010
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037
Katok, Anatole; Hertz, Federico Rodriguez
8
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
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 1192.37026
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
3
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
9
2008
New progress in nonuniform measure and cocycle rigidity. Zbl 1159.37316
Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez
4
2008
Moscow dynamics seminars of the nineteen seventies and the early career of Yasha Pesin. Zbl 1152.01009
Katok, Anatole
3
2008
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001
Katok, Anatole
46
2007
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017
Kalinin, Boris; Katok, Anatole
14
2007
Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data. Zbl 1136.37016
Katok, Anatole; Rodriguez Hertz, Federico
5
2007
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017
Katok, A.; Niţică, V.
5
2007
Local rigidity of restrictions of Weyl chamber flows. Zbl 1113.37015
Damjanović, Danijela; Katok, Anatole
3
2007
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004
Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
78
2006
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304
Katok, Anatole; Thouvenot, Jean-Paul
27
2006
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006
12
2006
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017
Einsiedler, Manfred; Katok, Anatole
19
2005
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029
Damjanović, Danijela; Katok, Anatole
16
2005
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023
Katok, Anatole; Katok, Svetlana
12
2005
Billiard table as a playground for a mathematician. Zbl 1147.37329
Katok, A. B.
5
2005
Constructions in elliptic dynamics. Zbl 1089.37012
Fayad, Bassam; Katok, Anatole
66
2004
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015
Damjanović, Danijela; Katok, Anatole
5
2004
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001
Hasselblatt, Boris; Katok, Anatole
99
2003
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001
Katok, Anatole
52
2003
Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023
Einsiedler, Manfred; Katok, Anatole
20
2003
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016
49
2002
Principal structures. Zbl 1047.37001
Hasselblatt, Boris; Katok, Anatole
26
2002
Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005
Katok, Anatole; Katok, Svetlana; Schmidt, Klaus
25
2002
Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029
Feres, Renato; Katok, Anatole
11
2002
Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029
Kalinin, Boris; Katok, Anatole
6
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.
36
2001
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016
Kalinin, Boris; Katok, Anatole
24
2001
Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
10
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
3
2001
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042
Katok, 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 1009.37013
Gunesch, Roland; Katok, Anatole B.
10
2000
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063
Guysinsky, M.; Katok, A.
25
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
142
1997
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009
Katok, Anatole; Thouvenot, Jean-Paul
51
1997
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010
Katok, A.; Spatzier, R. J.
49
1997
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021
Katok, A.; Spatzier, R. J.
57
1996
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082
Katok, A.; Kononenko, A.
32
1996
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038
Katok, A.; Lewis, J.
24
1996
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037
Katok, A.; Lewis, J.; Zimmer, R.
17
1996
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002
Katok, Anatole
5
1996
Nonstationary normal forms and rigidity of group actions. Zbl 0871.58073
Katok, A.; Spatzier, R. J.
3
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
31
1995
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039
Katok, Anatole; Katok, Svetlana
15
1995
The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015
Katok, Anatole B.; Schmidt, Klaus
8
1995
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027
Katok, Anatole; Spatzier, Ralf J.
60
1994
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029
Katok, Anatole; Burns, Keith
38
1994
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026
Katok, A.; Spatzier, R. J.
23
1994
Women in Soviet mathematics. Zbl 1194.01176
Katok, Anatole; Katok, Svetlana
3
1993
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024
Katok, A.
8
1992
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033
Flaminio, L.; Katok, A.
5
1992
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012
Katok, A.; Lewis, J.
36
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
21
1991
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034
Hurder, S.; Katok, A.
62
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
9
1990
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
8
1990
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053
Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.
49
1989
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050
Feres, Renato; Katok, Anatoly
10
1989
Vladimir Abramovich Rokhlin (23 August 1919 to 3 December 1984): Introductory note. Zbl 0688.01012
Katok, A.
2
1989
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042
Katok, Anatole
40
1988
Weakly mixing billiards. Zbl 0673.58028
Gutkin, E.; Katok, A.
5
1988
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040
Bernstein, David; Katok, Anatole
39
1987
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020
Katok, A.
30
1987
Ergodic theory and Weil measures for foliations. Zbl 0645.57021
Hurder, S.; Katok, A.
17
1987
Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001
Katok, Anatole; Strelcyn, Jean-Marie
117
1986
Random perturbations of transformations of an interval. Zbl 0616.60064
Katok, A.; Kifer, Y.
19
1986
Manifolds with non-positive curvature. Zbl 0572.58019
Burns, K.; Katok, A.
49
1985
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016
Katok, Anatole
17
1984
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015
Hurder, S.; Katok, A.
7
1984
On local entropy. Zbl 0533.58020
Brin, M.; Katok, A.
164
1983
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032
Katok, A.
12
1983
Entropy and closed geodesics. Zbl 0525.58027
Katok, A.
62
1982
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048
Katok, A.
43
1982
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029
Gerber, Marlies; Katok, Anatole
13
1982
Ergodic theory and dynamical systems II. Proceedings, special year, Maryland 1979-80. Zbl 0483.00005
2
1982
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021
Brin, M. I.; Feldman, J.; Katok, A.
14
1981
Dynamical systems with hyperbolic structure. Zbl 0598.58031
Katok, A. B.
5
1981
Ergodic theory and dynamical systems I. Proceedings, Special Year, Maryland 1979-80. Zbl 0451.00006
2
1981
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015
Katok, A.
467
1980
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009
Katok, Anatole
57
1980
...and 24 more Documents
all top 5

Cited by 3,085 Authors

36 Katok, Anatole
29 Morales Rojas, Carlos Arnoldo
25 Barreira, Luis Manuel
24 de la Llave, Rafael
24 Pesin, Yakov Borisovich
24 Varandas, Paulo
23 Rodriguez-Hertz, Federico
22 Troubetzkoy, Serge Eugene
21 Einsiedler, Manfred Leopold
20 Chen, Ercai
20 Huang, Wen
20 Lindenstrauss, Elon
20 Sun, Wenxiang
19 Fayad, Bassam R.
19 Gelfert, Katrin Grit
19 Pollicott, Mark
19 Zhao, Yun
18 Cao, Yongluo
18 Kanigowski, Adam
18 Kuznetsov, Sergey P.
18 Valls Anglés, Cláudia
17 Kalinin, Boris
17 Sadovskaya, Victoria
17 Tian, Xueting
16 Forni, Giovanni
16 Frączek, Krzysztof Marek
16 Oertel-Jäger, Tobias Hendrik
16 Kunde, Philipp
16 Lemańczyk, Mariusz
16 Mesón, Alejandro M.
16 Vericat, Fernando
16 Yang, Jiagang
16 Young, Lai-Sang
15 Climenhaga, Vaughn
15 Damjanović, Danijela
15 Kolesov, Andreĭ Yur’evich
15 Ledrappier, François
15 Paternain, Gabriel Pedro
14 Baladi, Viviane
14 Buzzi, Jérôme
14 Dragičević, Davor
14 Glyzin, Sergeĭ Dmitrievich
14 Gutkin, Eugene
14 Hasselblatt, Boris
14 Mihailescu, Eugen Gh.
14 Ryzhikov, Valeriĭ Valentinovich
14 Spatzier, Ralf J.
13 Avila, Artur
13 Chaika, Jonathan
13 Crovisier, Sylvain
13 Dolgopyat, Dmitry
13 Duan, Huagui
13 Gogolev, Andrey
13 Knieper, Gerhard
13 Stoyanov, Luchezar N.
13 Ulcigrai, Corinna
13 Zhu, Yujun
12 Bonatti, Christian
12 Bunimovich, Leonid Abramovich
12 Vetokhin, Alexandr N.
11 Araújo, Vítor
11 Cheng, Wenchiao
11 Ferenczi, Sébastien
11 Grines, Vyacheslav Zigmundovich
11 Guillarmou, Colin
11 Lefeuvre, Thibault
11 Li, Zhiming
11 Long, Yiming
11 Qin, Wenxin
11 Tien Cuong Dinh
11 Wilkinson, Amie
11 Xu, Leiye
11 Ye, Xiangdong
10 Bessa, Mário
10 Chernov, Nikolai Ivanovich
10 Giona, Massimiliano
10 Gorodetskii, Anton Semenovich
10 Kawan, Christoph
10 Le Calvez, Patrice
10 Liu, Hui
10 Liu, Lei
10 Llibre, Jaume
10 Masur, Howard A.
10 Potrie, Rafael
10 Shu, Lin
10 Viana, Marcelo
10 Wang, Wei
10 Wang, Zhenqi Jenny
10 Weiss, Howard
10 Wu, Weisheng
10 Zhou, Xiaoyao
10 Zhou, Yunhua
9 Backes, Lucas H.
9 Boyland, Philip L.
9 Burns, Keith
9 de Thélin, Henry
9 Del Magno, Gianluigi
9 Díaz, Lorenzo Justiniano
9 Ginzburg, Viktor L’vovich
9 Gürel, Basak Zehra
...and 2,985 more Authors
all top 5

Cited in 424 Serials

287 Ergodic Theory and Dynamical Systems
122 Discrete and Continuous Dynamical Systems
120 Communications in Mathematical Physics
101 Israel Journal of Mathematics
100 Transactions of the American Mathematical Society
91 Proceedings of the American Mathematical Society
90 Journal of Differential Equations
83 Physica D
82 Journal of Statistical Physics
78 Nonlinearity
73 Inventiones Mathematicae
72 Advances in Mathematics
60 Journal of Modern Dynamics
53 Dynamical Systems
52 Journal of Mathematical Analysis and Applications
50 Annales de l’Institut Fourier
45 Duke Mathematical Journal
42 Journal of Dynamics and Differential Equations
37 Mathematische Zeitschrift
36 Mathematical Notes
34 Annals of Mathematics. Second Series
33 Journal d’Analyse Mathématique
32 Chaos, Solitons and Fractals
31 Geometriae Dedicata
31 Mathematische Annalen
31 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
30 Topology and its Applications
30 Chaos
30 Regular and Chaotic Dynamics
30 Qualitative Theory of Dynamical Systems
27 Geometric and Functional Analysis. GAFA
27 Journal of Mathematical Sciences (New York)
24 Bulletin of the American Mathematical Society. New Series
24 Journal of the European Mathematical Society (JEMS)
24 Journal of Dynamical and Control Systems
24 SIAM Journal on Applied Dynamical Systems
23 Geometry & Topology
22 Acta Mathematica Sinica. English Series
21 Functional Analysis and its Applications
21 Journal of Functional Analysis
21 Journal of the American Mathematical Society
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
20 Stochastics and Dynamics
20 Proceedings of the Steklov Institute of Mathematics
19 Comptes Rendus. Mathématique. Académie des Sciences, Paris
18 Commentarii Mathematici Helvetici
18 Monatshefte für Mathematik
18 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
17 Physics Letters. A
17 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
17 Journal of Difference Equations and Applications
16 Annales Henri Poincaré
15 Bulletin de la Société Mathématique de France
15 Bulletin of the Brazilian Mathematical Society. New Series
14 Communications in Nonlinear Science and Numerical Simulation
13 Science China. Mathematics
12 Mathematical Proceedings of the Cambridge Philosophical Society
12 Journal of Geometry and Physics
12 Publications Mathématiques
12 Journal of Nonlinear Science
12 Calculus of Variations and Partial Differential Equations
12 Discrete and Continuous Dynamical Systems. Series B
12 Journal of Fixed Point Theory and Applications
12 Journal de l’École Polytechnique – Mathématiques
11 Journal of the London Mathematical Society. Second Series
11 Differential Equations
10 The Journal of Geometric Analysis
10 Electronic Research Announcements of the American Mathematical Society
9 Journal of Mathematical Physics
9 Bulletin of the London Mathematical Society
9 Compositio Mathematica
9 Memoirs of the American Mathematical Society
8 Russian Mathematical Surveys
8 Theoretical Computer Science
8 Systems & Control Letters
8 Differential Geometry and its Applications
8 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
8 Journal of Dynamical Systems and Geometric Theories
8 Journal of the Institute of Mathematics of Jussieu
8 Journal of Topology and Analysis
7 Automatica
7 Experimental Mathematics
7 Conformal Geometry and Dynamics
7 Arnold Mathematical Journal
6 Archive for Rational Mechanics and Analysis
6 Moscow University Mathematics Bulletin
6 Fundamenta Mathematicae
6 Indiana University Mathematics Journal
6 Journal de Mathématiques Pures et Appliquées. Neuvième Série
6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
6 Annales de l’Institut Henri Poincaré. Physique Théorique
6 Sbornik: Mathematics
6 Algebraic & Geometric Topology
6 Acta Mathematica Scientia. Series B. (English Edition)
6 Russian Journal of Nonlinear Dynamics
5 Journal of Computational Physics
5 Journal of Mathematical Biology
5 Physica A
5 Reports on Mathematical Physics
5 Studia Mathematica
...and 324 more Serials
all top 5

Cited in 63 Fields

2,892 Dynamical systems and ergodic theory (37-XX)
390 Differential geometry (53-XX)
346 Measure and integration (28-XX)
197 Ordinary differential equations (34-XX)
187 Manifolds and cell complexes (57-XX)
177 Global analysis, analysis on manifolds (58-XX)
159 General topology (54-XX)
142 Topological groups, Lie groups (22-XX)
142 Probability theory and stochastic processes (60-XX)
141 Mechanics of particles and systems (70-XX)
132 Number theory (11-XX)
124 Several complex variables and analytic spaces (32-XX)
112 Partial differential equations (35-XX)
94 Statistical mechanics, structure of matter (82-XX)
85 Operator theory (47-XX)
84 Group theory and generalizations (20-XX)
68 Quantum theory (81-XX)
66 Systems theory; control (93-XX)
64 Functions of a complex variable (30-XX)
52 Computer science (68-XX)
50 Biology and other natural sciences (92-XX)
48 Fluid mechanics (76-XX)
44 Information and communication theory, circuits (94-XX)
43 Functional analysis (46-XX)
43 Numerical analysis (65-XX)
39 Algebraic geometry (14-XX)
35 Difference and functional equations (39-XX)
31 Combinatorics (05-XX)
27 Convex and discrete geometry (52-XX)
26 Linear and multilinear algebra; matrix theory (15-XX)
24 Real functions (26-XX)
24 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
23 Algebraic topology (55-XX)
22 Geometry (51-XX)
20 Abstract harmonic analysis (43-XX)
20 Calculus of variations and optimal control; optimization (49-XX)
18 Statistics (62-XX)
15 Mathematical logic and foundations (03-XX)
12 General and overarching topics; collections (00-XX)
12 \(K\)-theory (19-XX)
12 Optics, electromagnetic theory (78-XX)
12 Geophysics (86-XX)
11 History and biography (01-XX)
10 Harmonic analysis on Euclidean spaces (42-XX)
10 Operations research, mathematical programming (90-XX)
8 Associative rings and algebras (16-XX)
8 Potential theory (31-XX)
8 Mechanics of deformable solids (74-XX)
7 Classical thermodynamics, heat transfer (80-XX)
7 Relativity and gravitational theory (83-XX)
6 Order, lattices, ordered algebraic structures (06-XX)
5 Category theory; homological algebra (18-XX)
4 Special functions (33-XX)
3 Field theory and polynomials (12-XX)
3 Commutative algebra (13-XX)
3 Nonassociative rings and algebras (17-XX)
3 Integral transforms, operational calculus (44-XX)
2 General algebraic systems (08-XX)
2 Integral equations (45-XX)
2 Astronomy and astrophysics (85-XX)
1 Sequences, series, summability (40-XX)
1 Approximations and expansions (41-XX)
1 Mathematics education (97-XX)

Citations by Year

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.