Anatole Katok
#16,242
Most Influential Person Now
American mathematician
Anatole Katok's AcademicInfluence.com Rankings
Anatole Katokmathematics Degrees
Mathematics
#1032
World Rank
#1767
Historical Rank
#451
USA Rank
Measure Theory
#1316
World Rank
#1659
Historical Rank
#467
USA Rank
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Mathematics
Anatole Katok's Degrees
- PhD Mathematics Moscow State University
Why Is Anatole Katok Influential?
(Suggest an Edit or Addition)According to Wikipedia, Anatoly Borisovich Katok was an American mathematician with Russian-Jewish origins. Katok was the director of the Center for Dynamics and Geometry at the Pennsylvania State University. His field of research was the theory of dynamical systems.
Anatole Katok's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Lyapunov exponents, entropy and periodic orbits for diffeomorphisms (1980) (940)
- Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES (1995) (911)
- Introduction to the Modern Theory of Dynamical Systems: PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS (1995) (458)
- Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION (1995) (434)
- On local entropy (1983) (348)
- Invariant Manifolds, Entropy and Billiards: Smooth Maps With Singularities (1986) (330)
- Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION: WHAT IS LOW-DIMENSIONAL DYNAMICS? (1995) (323)
- A First Course in Dynamics: with a Panorama of Recent Developments (2003) (257)
- APPROXIMATIONS IN ERGODIC THEORY (1967) (227)
- Invariant measures and the set of exceptions to Littlewood's conjecture (2006) (213)
- Entropy and closed geodesies (1982) (206)
- First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity (1994) (188)
- ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS (1973) (181)
- Invariant measures for higher-rank hyperbolic abelian actions (1996) (180)
- Interval exchange transformations and some special flows are not mixing (1980) (161)
- Bernoulli Diffeomorphisms on surfaces (1979) (151)
- FIFTY YEARS OF ENTROPY IN DYNAMICS: 1958-2007 (2007) (141)
- Constructions in elliptic dynamics (2004) (127)
- Combinatorial constructions in ergodic theory and dynamics (2003) (114)
- Differentiability and analyticity of topological entropy for Anosov and geodesic flows (1989) (112)
- Introduction to the Modern Theory of Dynamical Systems: Low-dimensional phenomena (1995) (110)
- Some remarks on Birkhoff and Mather twist map theorems (1982) (109)
- Four applications of conformal equivalence to geometry and dynamics (1988) (105)
- Slow entropy type invariants and smooth realization of commuting measure-preserving transformations (1997) (101)
- The growth rate for the number of singular and periodic orbits for a polygonal billiard (1987) (95)
- Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems (1994) (93)
- Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonians (1987) (86)
- Cocycles' stability for partially hyperbolic systems (1996) (86)
- Introduction to the Modern Theory of Dynamical Systems: PREFACE (1995) (82)
- Global rigidity results for lattice actions on tori and new examples of volume-preserving actions (1996) (76)
- Caustics for inner and outer billiards (1995) (73)
- Subelliptic Estimates of Polynomial Differential Operators and Applications to Rigidity of Abelian Actions (1994) (70)
- MONOTONE EQUIVALENCE IN ERGODIC THEORY (1977) (68)
- Ergodic theory and Weil measures for foliations (1987) (66)
- Expansive homeomorphisms of compact surfaces are pseudo-Anosov (65)
- Smooth Ergodic Theory and Its Applications (2001) (64)
- Introduction to the Modern Theory of Dynamical Systems: LOCAL HYPERBOLIC THEORY AND ITS APPLICATIONS (1995) (58)
- Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows (1991) (56)
- Theory of dynamical systems and general transformation groups with invariant measure (1977) (56)
- Rigidity of measurable structure for Z^d-actions by automorphisms of a torus (2000) (54)
- Local rigidity of partially hyperbolic actions I. KAM method and ${\mathbb Z^k}$ actions on the torus (2010) (52)
- Smooth models of Thurston's pseudo-Anosov maps (1982) (52)
- Higher cohomology for Abelian groups of toral automorphisms (1995) (46)
- Rigidity of measures—The high entropy case and non-commuting foliations (2005) (46)
- Rigidity of measurable structure for $\mathbb Z^d$-actions by automorphisms of a torus (2002) (44)
- Corrections to ‘Invariant measures for higher-rank hyperbolic abelian actions’ (1998) (43)
- Non-abelian cohomology of abelian Anosov actions (2000) (43)
- NONUNIFORM MEASURE RIGIDITY (2008) (41)
- Invariant Measures for Actions of Higher Rank Abelian Groups (2010) (41)
- Metric properties of measure preserving homeomorphisms (1970) (40)
- PERIODIC CYCLE FUNCTIONALS AND COCYCLE RIGIDITY FOR CERTAIN PARTIALLY HYPERBOLIC R ACTIONS (2005) (37)
- Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents (1981) (36)
- MEASURE RIGIDITY BEYOND UNIFORM HYPERBOLICITY: INVARIANT MEASURES FOR CARTAN ACTIONS ON TORI (2006) (35)
- Local Rigidity of Partially Hyperbolic Actions. II: The Geometric Method and Restrictions of Weyl Chamber Flows on SL(n, ℝ)/Γ (2010) (35)
- OPEN PROBLEMS IN DYNAMICS AND RELATED FIELDS (2007) (32)
- Introduction to the Modern Theory of Dynamical Systems: TRANSVERSALITY AND GENERICITY (1995) (31)
- Periodic cycle functions and cocycle rigidity for certain partially hyperbolic $\mathbb R^k$ actions (2005) (30)
- Chapter 1 Principal structures (2002) (28)
- Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem (2011) (28)
- Some new cases of realization of spectral multiplicity function for ergodic transformations (2009) (28)
- Anosov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature (1990) (27)
- Local rigidity of homogeneous parabolic actions: I. A model case (2011) (27)
- Spectral properties of dynamical systems with an integral invariant on the torus (1967) (25)
- Local rigidity of actions of higher rank abelian groups and KAM method (2004) (25)
- Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure (1999) (25)
- Smooth Non-Bernoulli K-Automorphisms (1980) (25)
- MIXED SPECTRUM REPARAMETERIZATIONS OF LINEAR FLOWS ON T 2 (2001) (24)
- Chapter 9 Ergodic theory and dynamics of G-spaces (with special emphasis on rigidity phenomena) (2002) (24)
- Periodic and Quasi-Periodic Orbits for Twist Maps (2020) (24)
- Rigidity in Higher Rank Abelian Group Actions: Introduction: an overview (2011) (23)
- Secondary classes and transverse measure theory of a foliation (1984) (23)
- Differentiability of entropy for Anosov and geodesic flows (1990) (23)
- Entropy and approximations of dynamical systems by periodic transformations (1967) (22)
- Nonuniform Hyperbolicity and Structure o Smooth Dynamical Systems (2010) (22)
- Weakly mixing billiards (1988) (20)
- Ergodic Theory and Dynamical Systems II (1982) (20)
- Flexibility of entropies for surfaces of negative curvature (2017) (19)
- The cohomology of expansive ℤd-actions by automorphisms of compact, abelian groups (1995) (19)
- UNIQUENESS OF LARGE INVARIANT MEASURES FOR Z k ACTIONS WITH CARTAN HOMOTOPY DATA (2007) (18)
- Measure theory through dynamical eyes (2012) (17)
- Higher cohomology for abelian groups of toral automorphisms II: the partially hyperbolic case, and corrigendum (2005) (17)
- Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank abelian groups (2010) (17)
- Invariant measures on G/Γ for split simple Lie groups G (2003) (17)
- Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov (2017) (17)
- Minimal Orbits for Small Perturbations of Completely Integrable Hamiltonian Systems (1992) (16)
- The Fried Average Entropy and Slow Entropy for Actions of Higher Rank Abelian Groups (2013) (16)
- Analytic uniquely ergodic volume preserving maps on odd spheres (2013) (15)
- Measurable rigidity and disjointness for {\mathbb Z}^k actions by toral automorphisms (2002) (14)
- From Groups to Geometry and Back (2017) (14)
- LOCAL RIGIDITY OF PARTIALLY HYPERBOLIC ACTIONS OF Z AND R, k ≥ 2. I. KAM METHOD AND ACTIONS ON THE TORUS (2004) (14)
- Lectures on surfaces (2008) (13)
- Nonstationary normal forms and rigidity of group actions (1996) (13)
- A First Course in Dynamics: Contents (2003) (12)
- The development of dynamics in the 20th century and the contribution of Jürgen Moser (2002) (12)
- Hyperbolic measures and commuting maps in low dimension (1996) (11)
- Local rigidity of restrictions of Weyl chamber flows (2007) (10)
- Flexibility of Lyapunov exponents (2019) (10)
- Rigidity of higher rank abelian cocycles with values in diffeomorphism groups (2007) (10)
- Entropy and growth of expanding periodic orbits for one-dimensional maps (1998) (10)
- A First Course in Dynamics: Variational Methods, Twist Maps, and Closed Geodesics (2003) (9)
- A First Course in Dynamics: APPENDIX (2003) (9)
- Survey on entropy-type invariants of sub-exponential growth in dynamical systems (2020) (8)
- Moscow dynamics seminars of the Nineteen seventies and the early career of Yasha Pesin (2008) (8)
- Arithmeticity and topology of smooth actions of higher rank abelian groups (2013) (8)
- Introduction to the Modern Theory of Dynamical Systems: SMOOTH MAPS OF THE INTERVAL (1995) (7)
- Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program (2010) (7)
- Three Papers on Dynamical Systems (1981) (6)
- FIVE MOST RESISTANT PROBLEMS IN DYNAMICS (2004) (6)
- Errata to "Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori" and "Uniqueness of large invariant measures for $\Zk$ actions with Cartan homotopy data" (2010) (5)
- Rigidity for Cartan Actions of Higher Rank Lattices (1991) (5)
- Ergodic theory and dynamical systems: Proceedings, special year, Maryland 1979-80 (1981) (5)
- Rigidity in Higher Rank Abelian Group Actions: Contents (2011) (4)
- Introduction to the Modern Theory of Dynamical Systems: STATISTICAL BEHAVIOR OF ORBITS AND INTRODUCTION TO ERGODIC THEORY (1995) (3)
- Rigidity in Higher Rank Abelian Group Actions: Cocycles, cohomology, and rigidity (2011) (3)
- OPEN PROBLEMS IN ELLIPTIC DYNAMICS (2009) (3)
- Local Rigidity of Partially Hyperbolic Actions: Solution of the General Problem via KAM Method (2011) (2)
- Introduction to the Modern Theory of Dynamical Systems: CONTINUOUS MAPS OF THE INTERVAL (1995) (2)
- Smooth ergodic theory and its applications : proceedings of the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications July 26-August 13, 1999, University of Washington, Seattle (2001) (2)
- MASS program at penn state (2002) (2)
- Introduction to the Modern Theory of Dynamical Systems: HOMEOMORPHISMS OF THE CIRCLE (1995) (2)
- A First Course in Dynamics: Entropy and Chaos (2003) (2)
- Introduction to the Modern Theory of Dynamical Systems: EQUIVALENCE, CLASSIFICATION, AND INVARIANTS (1995) (1)
- Introduction and cocycle problem (2011) (1)
- A First Course in Dynamics: PANORAMA OF DYNAMICAL SYSTEMS (2003) (1)
- Introduction to the Modern Theory of Dynamical Systems: SURVEY OF EXAMPLES (1995) (1)
- PARTIALLY HYPERBOLIC PHENOMENA IN DYNAMICAL SYSTEMS WITH DESCRETE AND CONTINUOUS TIME (1)
- Introduction to the Modern Theory of Dynamical Systems: NOTES (1995) (1)
- A First Course in Dynamics: Recurrence and Equidistribution in Higher Dimension (2003) (0)
- A First Course in Dynamics: Preface (2003) (0)
- A First Course in Dynamics: Simple Systems with Complicated Orbit Structure (2003) (0)
- A First Course in Dynamics: Linear Maps and Linear Differential Equations (2003) (0)
- A First Course in Dynamics: A COURSE IN DYNAMICS: FROM SIMPLE TO COMPLICATED BEHAVIOR (2003) (0)
- A First Course in Dynamics: Introduction (2003) (0)
- Part I. Approximation and genericity in ergodic theory (2003) (0)
- A First Course in Dynamics: Recurrence and Equidistribution on the Circle (2003) (0)
- A First Course in Dynamics: Simple Dynamics as a Tool (2003) (0)
- A First Course in Dynamics: Hyperbolic Dynamics (2003) (0)
- Some properties of ultrametric spaces and their relations to category theory and computer science (2002) (0)
- Part II. Cocycles, cohomology and combinatorial constructions (2003) (0)
- Anatole Katok Interview December 1980 & January 1981 (1980) (0)
- Topology and smooth structure revisited (2008) (0)
- A First Course in Dynamics: Solutions (2003) (0)
- Introduction to the Modern Theory of Dynamical Systems: METRIC STRUCTURE OF HYPERBOLIC SETS (1995) (0)
- Lectures on Groups and Their Connections to Geometry (2009) (0)
- First cohomology and rigidity for general cocycles (2011) (0)
- MULTIPLICATIVE PROPERTIES OF AUTOMORPHISMS (2011) (0)
- Introduction to the Modern Theory of Dynamical Systems: REFERENCES (1995) (0)
- Anatole Katok Interview January 1981 (1981) (0)
- Various ways of representing surfaces and basic examples (2008) (0)
- Ergodic Theory and Geometric Rigidity and Number Theory 5 January to 7 July 2000 Report from the Organisers (2014) (0)
- NONSTATIONARY NORMAL FORMS AND RIGIDITY OFGROUP (1996) (0)
- Introduction to the Modern Theory of Dynamical Systems: FLOWS ON SURFACES AND RELATED DYNAMICAL SYSTEMS (1995) (0)
- Rigidity in Higher Rank Abelian Group Actions: Definitions and general properties of abelian group actions (2011) (0)
- Introduction to the Modern Theory of Dynamical Systems: Appendix: BACKGROUND MATERIAL (1995) (0)
- Lectures on Lyapunov Exponents (2014) (0)
- A First Course in Dynamics: Conservative Systems (2003) (0)
- A First Course in Dynamics: Strange Attractors (2003) (0)
- A First Course in Dynamics: Quadratic Maps (2003) (0)
- INVARIANT MEASURES ON SL(n; R)=¡ (1996) (0)
- Introduction to the Modern Theory of Dynamical Systems: TOPOLOGICAL PROPERTIES OF HYPERBOLIC SETS (1995) (0)
- Introduction to the Modern Theory of Dynamical Systems: FIRST EXAMPLES (1995) (0)
- A First Course in Dynamics: Systems with Stable Asymptotic Behavior (2003) (0)
- A First Course in Dynamics: Dynamics, Number Theory, and Diophantine Approximation (2003) (0)
- Introduction to the Modern Theory of Dynamical Systems: HINTS AND ANSWERS TO THE EXERCISES (1995) (0)
- A First Course in Dynamics: Hints and Answers (2003) (0)
- Introduction to the Modern Theory of Dynamical Systems: ORBIT GROWTH ARISING FROM TOPOLOGY (1995) (0)
- Rigidity in Higher Rank Abelian Group Actions: First cohomology and rigidity for vector-valued cocycles (2011) (0)
- AN OVERVIEW OF BASIC TOPICS IN TOPOLOGY AND RELATED AREAS OF GEOMETRY (0)
- Introduction to the Modern Theory of Dynamical Systems: VARIATIONAL ASPECTS OF DYNAMICS (1995) (0)
- Introduction to the Modern Theory of Dynamical Systems: SYSTEMS WITH SMOOTH INVARIANT MEASURES AND MORE EXAMPLES (1995) (0)
- Ergodic Theory and Geometric Rigidity and Number Theory (2014) (0)
- Combinatorial structure and topological classification of surfaces (2008) (0)
- Differentiable structure on surfaces: Real and complex (2008) (0)
- Anatole Katok Interview December 27, 1982 (1982) (0)
- Rigidity in Higher Rank Abelian Group Actions: Higher order cohomology (2011) (0)
- Introduction to the Modern Theory of Dynamical Systems: TWIST MAPS (1995) (0)
- Anatole and Svetlana Katok Interview October 29 & 31, 1999 (1999) (0)
- A First Course in Dynamics: Reading (2003) (0)
- Rigidity in Higher Rank Abelian Group Actions: Principal classes of algebraic actions (2011) (0)
- Rigidity in Higher Rank Abelian Group Actions: Preparatory results from analysis (2011) (0)
- Introduction to the Modern Theory of Dynamical Systems: CIRCLE DIFFEOMORPHISMS (1995) (0)
- ERGODIC THEORY FROM HUMSAN TO VIENNA (2006) (0)
- A First Course in Dynamics: Homoclinic Tangles (2003) (0)
- Rigidity in Higher Rank Abelian Group Actions: References (2011) (0)
- The Fried Average Entropy and Slow Entropy for Actions of Higher Rank Abelian Groups (2014) (0)
- Riemannian metrics and geometry of surfaces (2008) (0)
- Vladimir Abramovich Rokhlin (23 August 1919 to 3 December 1984): Introductory note (1989) (0)
- Flexibility of Lyapunov exponents with respect to two classes of measures on the torus (2019) (0)
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