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Sets of Invariant Measures and Cesaro StabilitySergey Kryzhevich, 2017, original scientific article
Abstract: We take a space X of dynamical systems that could be: homeomorphisms or continuous maps of a compact metric space K or diffeomorphisms of a smooth manifold or actions of an amenable group. We demonstrate that a typical dynamical system of X is a continuity point for the set of probability invariant measures considered as a function of a map, let Y be the set of all such continuity points. As a corollary we prove that for typical dynamical systems average values of continuous functions calculated along trajectories do not drastically change if the system is perturbed.
Keywords: ergodic theory, invariant measures, shadowing, stability, tolerance stability, topological dynamics
Published in RUNG: 02.10.2017; Views: 4691; Downloads: 0
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