Item description for Positive Transfer Operators and Decay of Correlations (Advanced Series in Nonlinear Dynamics, Volume 16) by Viviane Baladi...
Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system "mixes", i.e. "forgets" its initial conditions.
This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.
The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.
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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 0.75" Width: 6.25" Height: 8.5" Weight: 1.25 lbs.
Publisher World Scientific Publishing Company
ISBN 9810233280 ISBN13 9789810233280
Reviews - What do customers think about Positive Transfer Operators and Decay of Correlations (Advanced Series in Nonlinear Dynamics, Volume 16)?
An operator with nine lives. Jul 28, 2002
The "transfer operator" has many incarnations (and many names). It has emerged and re-emerged, over the years, in a rich variety of applications. The basic idea behind it is in fact quite clear from the familiar and classical Perron-Frobenius theorem for positive matrices. But Baladi's lovely book deals with the infinite-dimensional case, where the applications are, if possible--, even more striking. The starting point there was the powerful use David Ruelle first made of it in the sixties in his study of phase-transition problems in quantum statistical mechanics. The work leading to the Perron-Frobenius-Ruelle theorem!-- Since then, it has re-emerged in a rich variety of applications in dynamics; both continuous and discrete;-- both experimental and symbolic;-- being central in our (limited) understanding of attractors! It is used both in applications (wavelets, fractals, ...),and in pure math (Zeta functions, and trace formulas, to mention only a few such examples). It is all clearly and wonderfully presented in Baladi's book, which now serves as a lucid introduction to a rich and exciting set of new trends in the research literature.