Advanced Series in Nonlinear Dynamics - Vol. 16
POSITIVE TRANSFER OPERATORS AND DECAY OF CORRELATIONS
by Viviane Baladi (CNRS, Université de Paris-Sud, France)
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.
Contents:
- Subshifts of Finite Type: A Key Symbolic Model
- Smooth
Uniformly Expanding Dynamics
- Piecewise Expanding Systems
- Hyperbolic Systems
Readership: Physicists, mathematicians, interdisciplinary scientists
and social scientists.
"The book can be used both as a textbook for beginners and as a reference book for workers in the field ... the proofs are given in full, allowing a detailed study of the techniques and making the book nicely self-contained."
| Mathematical Reviews, 2001 |
| 324pp |
Pub. date: Jul 2000 |
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