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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.
List of contents
1 General Qualitative Properties.- 2 Ergodicity and Ergodic Points.- 3 Entropy and Complexity.- 4 Markovian Pavements.- 5 Gibbs Distributions.- 6 General Properties of Gibbs and SRB Distributions.- 7 Analyticity, Singularity and Phase Transitions.- 8 Special Ergodic Theory Problems in Nonchaotic Dynamics.- 9 Some Special Topics in KAM Theory.- 10 Special Problems in Chaotic Dynamics.- A Nonequilibrium Thermodynamics? Twenty-Seven Comments.- Name Index.- Citations Index.
Summary
Intended for beginners in ergodic theory, this introductory textbook 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 Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Additional text
From the reviews:
"The book is centered on the symbiotic relationship between ergodic theory and statistical mechanics, in particular on its modern applications to chaotic and non-chaotic dynamical systems. In slightly more than 400 pages the authors … discuss in detail important applications of the theory. This is achieved by treating many important and interesting questions as ‘guided problems’ … . the entire book is tightly and nicely knitted together." (Luc Rey-Bellet, Mathematical Reviews, 2005h)
"The main novelty is the systematic treatment of a few characteristic problems of ergodic theory by a unified method in terms of convergent or divergent power series expansions. … The problems at the end of every section are an essential complement to the text … ." (Nasir N. Ganikhodjaev, Zentralblatt MATH, Vol. 1065, 2005)
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From the reviews:
"The book is centered on the symbiotic relationship between ergodic theory and statistical mechanics, in particular on its modern applications to chaotic and non-chaotic dynamical systems. In slightly more than 400 pages the authors ... discuss in detail important applications of the theory. This is achieved by treating many important and interesting questions as 'guided problems' ... . the entire book is tightly and nicely knitted together." (Luc Rey-Bellet, Mathematical Reviews, 2005h)
"The main novelty is the systematic treatment of a few characteristic problems of ergodic theory by a unified method in terms of convergent or divergent power series expansions. ... The problems at the end of every section are an essential complement to the text ... ." (Nasir N. Ganikhodjaev, Zentralblatt MATH, Vol. 1065, 2005)
