Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES
- A. Katok, B. Hasselblatt
- Mathematics
- 1995
Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the…
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
- A. Katok
- Mathematics
- 1 December 1980
© Publications mathematiques de l’I.H.E.S., 1980, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.…
Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION
- A. Katok, B. Hasselblatt
- Economics
- 1995
Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION: WHAT IS LOW-DIMENSIONAL DYNAMICS?
- A. Katok, B. Hasselblatt
- Mathematics
- 1995
Introduction to the Modern Theory of Dynamical Systems: PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS
- A. Katok, B. Hasselblatt
- Mathematics
- 1995
Invariant measures and the set of exceptions to Littlewood's conjecture
- M. Einsiedler, A. Katok, E. Lindenstrauss
- Mathematics
- 22 December 2006
We classify the measures on SL (k,R)/SL (k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set…
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
- A. Katok, R. Spatzier
- Mathematics
- 1 December 1994
This is the first in a series of papers exploring rigidity properties of hyperbolic actions ofZk orRk fork ≥ 2. We show that for all known irreducible examples, the cohomology of smooth cocycles over…
APPROXIMATIONS IN ERGODIC THEORY
- A. Katok, A. M. Stepin
- Mathematics
- 31 October 1967
CONTENTSIntroductionPart I. The method of approximations § 1. Definitions and examples § 2. Approximations, ergodicity and mixing § 3. Approximations and the spectrum § 4. Approximations and entropy…
Entropy and closed geodesies
- A. Katok
- MathematicsErgodic Theory and Dynamical Systems
- 1 December 1982
Abstract We study asymptotic growth of closed geodesies for various Riemannian metrics on a compact manifold which carries a metric of negative sectional curvature. Our approach makes use of both…
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