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Title:Sets of Invariant Measures and Cesaro Stability
Authors:Kryzhevich, Sergey (Author)
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Work type:Not categorized (r6)
Tipology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
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
Year of publishing:2017
Number of pages:133-147
COBISS_ID:4924923 Link is opened in a new window
License:CC BY-NC-SA 4.0
This work is available under this license: Creative Commons Attribution Non-Commercial Share Alike 4.0 International
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Title:Differential Equations and Control Processes
Year of publishing:2017