The Diffusion Coefficient For Piecewise Expanding Maps Of The Interval With Metastable States

Dmitry Dolgopyat; Paul Wright

The Diffusion Coefficient For Piecewise Expanding Maps Of The Interval With Metastable States

Dynamical Systems 2010-11-25 v1 Mathematical Physics math.MP

Authors: Dmitry Dolgopyat , Paul Wright

Abstract

Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the subintervals lose their invariance in such a way that there is a unique ACIM, we show how to approximate the diffusion coefficient for an observable of bounded variation by the diffusion coefficient of a related continuous time Markov chain.

Keywords

piecewise expanding maps metastable states diffusion coefficient absolutely continuous invariant measures continuous time Markov chain bounded variation

Cite

@article{arxiv.1011.5330,
  title  = {The Diffusion Coefficient For Piecewise Expanding Maps Of The Interval With Metastable States},
  author = {Dmitry Dolgopyat and Paul Wright},
  journal= {arXiv preprint arXiv:1011.5330},
  year   = {2010}
}

Comments

12 pages, 1 figure. Dedicated to Manfred Denker on the occasion of his 60th birthday

The Diffusion Coefficient For Piecewise Expanding Maps Of The Interval With Metastable States

Abstract

Keywords

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