Non-stationary compositions of Anosov diffeomorphisms

Details Non-stationary compositions of Anosov diffeomorphisms Non-stationary compositions of Anosov diffeomorphisms

2011-12-13

arxiv.org/abs/1112.3065v1

Nonlinearity 24 (2011) 2991-3018

Mathematics

Dynamical Systems

Scientific paper

10.1088/0951-7715/24/10/016

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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