Positive Transfer Operators and Decay of Correlations.pdf

Positive Transfer Operators and Decay of Correlations

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, that is, 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.

of the transfer operator L upper bounds on the decay of correlations depend crucially on estimations of the probability of return to the origin of an auxiliary Markov chain, which are presented in Section A. 2 Definitions and statement of the results Let Abe a finite set henceforth called alphabet. Let us denote A = x= (x j) j≤−1,x∈ A (2.1) the set of sequences of elements of the

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9789810233280 ISBN
Positive Transfer Operators and Decay of Correlations.pdf


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Notes actuelles

Sofya Voigtuh

a clean discussion of exponential decay of correlations for Gibbs-Markov maps ( includes ... Viviane Baladi: Positive Transfer Operators and Decay of Correlation  ...

Mattio Müllers

System Upgrade on Tue, May 19th, 2020 at 2am (ET). During this period, E- commerce and registration of new users may not be available for up to 12 hours.

Noels Schulzen

We consider pairs of toral automorphisms (A,B) satisfying an invariant cone property. At each iteration, A acts with probability p∊(0,1) and B with probability 1−p. We prove exponential decay of correlations for a class of Hölder continuous observables.

Jason Leghmann

j such that for some k2Nthe transfer operator Lkmaps C j into C j+1 Received by the editors May 23, 1999 and, in revised form, January 13, 2000. 2000 Mathematics Subject Classi cation. Primary 37A25, 37C30, 37C40. Key words and phrases. Decay of correlations, tower, transfer operator, projective metrics. c 2001 American Mathematical Society 3371

Jessica Kolhmann