Title:  Sets of Invariant Measures and Cesaro Stability 

Authors:  Kryzhevich, Sergey (Author) 

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Language:  English 

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:  133147 

Numbering:  3 

COBISS_ID:  4924923 

URN:  URN:SI:UNG:REP:CGPCG6IR 

License:  This work is available under this license: Creative Commons Attribution NonCommercial Share Alike 4.0 International 

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