Bibliothèque de L'IMIST/CNRST

Includes bibliographical references (pages 411-421) and index.

1. General qualitative properties -- 1.1. Historical note -- 1.2. Examples and some definitions -- 1.3. Harmonic oscillators and integrable systems as dynamical systems -- 1.4. Frequencies of visit -- 2. Ergodicity and ergodic points -- 2.1. Quasi-periodic motions and integrability -- 2.2. Ergodic properties of quasi-periodic motions; Ergodic sequences and measures -- 2.3. Ergodic points -- 2.4. Ergodic decomposition -- 3. Entropy and complexity -- 3.1. Complexity of motions and entropy -- 3.2. The Shannon-McMillan theorem -- 3.3. Elementary properties of the average entropy -- 3.4. Further properties of the average entropy; Generator theorem -- 4. Markovian pavements -- 4.1. Compatibility of histories; Markovian pavements -- 4.2. Markovian pavements for hyperbolic systems -- 4.3. Coding of the volume measure of smooth hyperbolic systems -- 5. Gibbs distributions -- 5.1. Gibbs distributions -- 5.2. Properties of Gibbs distributions -- 5.3. Gibbs distributions on Z+ -- 5.4. An application: Expansive maps of [0,1] -- 6. General properties of Gibbs and SRB distributions -- 6.1. Variational properties of Gibbs distributions -- 6.2. Applications to Ansov systems; SRB distribution -- 6.3. Periodic orbits, invariant probability distributions and entropy -- 6.4. Equivalent potentials; Gibbs distributions with transitive vacuum -- 7. Analyticity, singularity and phase transitions -- 7.1. Polymers -- 7.2. Cluster expansions -- 7.3. Renormalization by decimation in one-dimensional systems -- 7.4. Absence of phase transitions: More criteria -- 7.5. Phase transitions -- 8. Special ergodic theory problems in nonchaotic dynamics -- 8.1. Theory of quasi-periodic Hamiltonian motions -- 8.2 Graphs and diagrams for the Lindstedt series -- 8.3. Cancellations -- 8.4. Convergence and the KAM theorem -- 9. Some special topics in KAM theory -- 9.1. Resummations and renormalized series for invariant tori -- 9.2. Bounds on renormalized series; Convergence -- 9.3. Scaling laws for the standard map -- 9.4. Limit function for the standard map near resonances -- 10. Special problems in chaotic dynamics -- 10.1. Perturbing Arnold's cat map -- 10.2. Extending systems; Lattices of Arnold's cat maps -- 10.3. Chaos in time: An SRB distribution -- 10.4. Chaos in space-time and SRB distributions -- 10.5. Isomorphisms -- Appendix A: Nonequilibrium thermodynamics? Twenty-seven comments.