Approximating invariant densities of metastable systems

Details Approximating invariant densities of metastable systems Approximating invariant densities of metastable systems

2009-05-02

arxiv.org/abs/0905.0223v1

Mathematics

Dynamical Systems

19 pages, 6 figures

Scientific paper

10.1017/S0143385710000337

We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed slightly to make the invariant sets merge, we describe how the unique ACIM of the perturbed map can be approximated by a convex combination of the two initial ergodic ACIMs.

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