Ergodic theory of smooth dynamical systems. (English. Russian original) Zbl 0781.58018
Dynamical systems. II. Ergodic theory with applications to dynamical systems and statistical mechanics. Encycl. Math. Sci. 2, 99-206 (1989); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 2, 113-231 (1985).
Contents: Chapter 6. Stochasticity of smooth dynamical systems. The elements of KAM-Theory (by Ya. G. Sinai). Chapter 7. General theory of smooth hyperbolic dynamical systems (by Ya. B. Pesin). Chapter 8. Dynamical systems of hyperbolic type with singularities (by L. A. Bunimovich). Chapter 9. Ergodic theory of one-dimensional mappings (by M. V. Yakobson). Bibliography.
For the entire collection see [Zbl 0778.00014].
For the entire collection see [Zbl 0778.00014].
MSC:
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37F50 | Small divisors, rotation domains and linearization in holomorphic dynamics |
