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arXiv · 1112.3065

Non-stationary compositions of Anosov diffeomorphisms

Mikko Stenlund
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Abstract

Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a 2-dimensional compact Riemannian manifold, which are allowed to change with time - slowly, but in a rather arbitrary fashion. In particular, such systems admit no invariant measure. By constructing a coupling, we prove that any two sufficiently regular distributions of the initial state converge exponentially with time. Thus, a system of the kind loses memory of its statistical history rapidly.

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Mikko Stenlund. 2011-12-13. Non-stationary compositions of Anosov diffeomorphisms. https://doi.org/10.1088/0951-7715%2F24%2F10%2F016

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