Thermodynamics of Chaotic Systems : An Introduction

Includes References (273-281) and Index

Part I. Essentials of Nonlinear Dynamics
1. Nonlinear mappings
2. Probability in the theory of chaotic systems
3. Symbolic dynamics
Part II. Essentials of Information Theory and Thermodynamics
4. The Shannon information
5. Further information measures
6. Generalized canonical distributions
7. The fundamental thermodynamic relations
8. Spin systems
Part III. Thermostatistics of Multifractals
9. Escort distributions
10. Fractals 11. Multifractals
12. Bit cumulants in multifractal distribution
13. Thermodynamics of a finite volume
Part IV. Dynamical Analysis of Chaotic Systems
14. Statistics of dynamical symbol sequences
15. Expansion rate and information loss
16. The topological pressure
17. Transfer operator methods
18. Repellers and escape
Part V. Advanced Thermodynamics
19. Thermodynamics of expanding maps
20. Thermodynamics with several intensive parameters
21. Phase transitions

This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. The most important invariants used to characterise chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and statistical mechanics. Among the subjects treated are: probabilistic aspects of chaotic dynamics; the symbolic dynamics technique; information measures, the maximum entropy principle; general thermodynamic relations; spin systems; fractals and multifractals; expansion rate and information loss; the topological pressure; transfer operator methods; and repellers and escape. The more advanced chapters deal with the thermodynamic formalism for expanding maps, the thermodynamic analysis of chaotic systems with several intensive parameters and phase transitions in nonlinear dynamics--Publisher's blurb.