Aspects of Ergodic, Qualitative and Statistical Theory of Motion
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Beschreibung
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.
The Italian 1980 version of Gallavotti's book on ergodic theory of maps is a classic and the scientific community will certainly welcome its rebirth in this completely rewritten and greatly enlarged English edition Includes supplementary material: sn.pub/extras
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.
Autor*in
Giovanni Gallavotti
Themen in »Aspects of Ergodic, Qualitative and Statistical Theory of Motion«
Asonov Theory Chaotic Dynamics Ergodic Theory of Maps Ergodicity Gibbs State KAM Theory Renormalization group mathematical physics
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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)
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