Ebook: Aspects of Ergodic, Qualitative and Statistical Theory of Motion
- Genre: Physics // Thermodynamics and Statistical Mechanics
- Tags: Analysis, Statistical Physics Dynamical Systems and Complexity, Theoretical Mathematical and Computational Physics, Classical Continuum Physics
- Series: Texts and Monographs in Physics
- Year: 2004
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Content:
Front Matter....Pages I-X
General Qualitative Properties....Pages 1-26
Ergodicity and Ergodic Points....Pages 27-71
Entropy and Complexity....Pages 73-108
Markovian Pavements....Pages 109-153
Gibbs Distributions....Pages 155-187
General Properties of Gibbs and SRB Distributions....Pages 189-226
Analyticity, Singularity and Phase Transitions....Pages 227-289
Special Ergodic Theory Problems in Nonchaotic Dynamics....Pages 291-325
Some Special Topics in KAM Theory....Pages 327-357
Special Problems in Chaotic Dynamics....Pages 359-396
Back Matter....Pages 397-438
Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Content:
Front Matter....Pages I-X
General Qualitative Properties....Pages 1-26
Ergodicity and Ergodic Points....Pages 27-71
Entropy and Complexity....Pages 73-108
Markovian Pavements....Pages 109-153
Gibbs Distributions....Pages 155-187
General Properties of Gibbs and SRB Distributions....Pages 189-226
Analyticity, Singularity and Phase Transitions....Pages 227-289
Special Ergodic Theory Problems in Nonchaotic Dynamics....Pages 291-325
Some Special Topics in KAM Theory....Pages 327-357
Special Problems in Chaotic Dynamics....Pages 359-396
Back Matter....Pages 397-438
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