CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY

1977/08/31 by Ya B Pesin, Ya. B. Pesin · 15 citations
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · doi:10.1070/rm1977v032n04abeh001639

crossref issued 1977/08/31 · crossref published 1977/08/31 · crossref published-print 1977/08/31 · openalex publication_date 1977/08/31 · crossref created 2005/11/08 · crossref published-online 2007/10/16 · crossref deposited 2024/10/03 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31

Abstract

CONTENTS Part I § 1. Introduction § 2. Prerequisites from ergodic theory § 3. Basic properties of the characteristic exponents of dynamical systems § 4. Properties of local stable manifolds Part II § 5. The entropy of smooth dynamical systems § 6. "Measurable foliations". Description of the π-partition § 7. Ergodicity of a diffeomorphism with non-zero exponents on a set of positive measure. The K -property § 8. The Bernoullian property § 9. Flows § 10. Geodesic flows on closed Riemannian manifolds without focal points References

Citations

• APPROXIMATIONS IN ERGODIC THEORY

Cited by

• Continuity of measure-theoretic entropy for stochastic differential equations
• Average measure theoretic entropy for a family of expanding on average random Blaschke products
• Beyond Point Particles -- Extended Structural Dynamics and the H Theorem
• Ergodic Theory: Basic Examples and Constructions
• Dynamic entropy as a measure of caging and persistent particle motion in supercooled liquids
• The Problem of Positive Kolmogorov-Sinai entropy for the Standard map
• Entropy production, dynamical localization and criteria for quantum chaos in the open quantum kicked rotor
• A review of linear response theory for general differentiable dynamical systems
• Thermodynamic Irreversibility from High-Dimensional Hamiltonian Chaos
• Mapping dynamical systems onto complex networks
• Synchronization and information transmission in spatio-temporal networks of deformable units
• Chaos edges ofz-logistic maps: Connection between the relaxation and sensitivity entropic indices
• On random linear dynamical systems in a Banach space. I. Multiplicative Ergodic Theorem and Krein-Rutmann type Theorems
• Convergence to the critical attractor of dissipative maps: Log-periodic oscillations, fractality, and nonextensivity
• Entropy-Related Extremum Principles for Model Reduction of Dissipative Dynamical Systems