Aspects of Ergodic, Qualitative and Statistical Theory of Motion

Giovanni Gallavotti, Federico Bonetto, Guido Gentile (Autoren)

Buch | Hardcover

X, 440 Seiten

2004 | 2004
Springer Berlin (Verlag)
978-3-540-40879-6 (ISBN)

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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	23.3.2004
Reihe/Serie	Theoretical and Mathematical Physics
Zusatzinfo	X, 440 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	780 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Asonov Theory • Bewegung (Physik) • chaotic dynamics • Ergodentheorie • Ergodicity • Ergodic Theory of Maps • Gibbs State • KAM Theory • Mathematical Physics • Renormalization Group
ISBN-10	3-540-40879-7 / 3540408797
ISBN-13	978-3-540-40879-6 / 9783540408796
Zustand	Neuware