Thermodynamics of Chaotic Systems An Introduction [Paperback]

This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems.Dealing with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems, the most important invariants used to characterize chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and statistical mechanics.Dealing with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems, the most important invariants used to characterize chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and statistical mechanics.This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. The most important invariants used to characterize 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, repellers and escape. The more advanced chapters deal with the thermodynamic formalism for expanding maps, thermodynamic analysis of chaotic systems with several intensive parameters, and phase transitions in nonlinear dynamics.Introduction; 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 multifraclsP