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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
ESSENTIALS OF NONLINEAR DYNAMICS
Nonlinear mappings
Probability in the theory of chaotic systems
Symbolic dynamics
ESSENTIALS OF INFORMATION THEORY AND THERMODYNAMICS
The Shannon information
Further information measures
Generalized canonical distributions
The fundamental thermodynamic relations
Spin systems
THERMOSTATISTICS OF MULTIFRACTALS
Escort distributions
Fractals
Multifractals
Bit-cumulants in multifractal statistics
Thermodynamics of finite volume
DYNAMICAL ANALYSIS OF CHAOTIC SYSTEMS
Statistics of dynamical symbol sequences
Expansion rate and information loss
The topological pressure
Transfer operator methods
Repellers and escape
ADVANCED THERMODYNAMICS
Thermodynamics of expanding maps
Thermodynamics with several intensive parameters
Phase transitions