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Aspects of Ergodic, Qualitative and Statistical Theory of Motion - Giovanni Gallavotti, Federico Bonetto, Guido Gentile

Aspects of Ergodic, Qualitative and Statistical Theory of Motion

Buch | Softcover
X, 440 Seiten
2010 | 1. Softcover reprint of hardcover 1st ed. 2004
Springer Berlin (Verlag)
978-3-642-07416-5 (ISBN)
CHF 149,75 inkl. MwSt
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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.

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.

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)

Erscheint lt. Verlag 19.10.2010
Reihe/Serie Theoretical and Mathematical Physics
Zusatzinfo X, 440 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 667 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie Astronomie / Astrophysik
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Asonov Theory • chaotic dynamics • Ergodicity • Ergodic Theory of Maps • Gibbs State • KAM Theory • Mathematical Physics • Renormalization Group
ISBN-10 3-642-07416-2 / 3642074162
ISBN-13 978-3-642-07416-5 / 9783642074165
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