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

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

2010-11-24

arxiv.org/abs/1011.5330v1

Mathematics

Dynamical Systems

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

Scientific paper

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.

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