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Positive Transfer Operators and ...(V16)
Hardcover
Series: Advanced Nonlinear Dynamics, Book 16
ISBN13: 9789810233280
Publisher: World Scientific Publishing Company
Published: Jul 22 2000
Pages: 324
Weight: 1.23
Height: 0.85 Width: 6.53 Depth: 8.59
Language: English
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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