Author： Stenlund Mikko
Publisher： IOP Publishing
ISSN： 0951-7715
Source： Nonlinearity, Vol.24, Iss.10, 2011-10, pp. : 2991-3018
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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 two-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 this kind loses memory of its statistical history rapidly.
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