ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Sets of Invariant Measures and Cesaro Stability


Sergey Gennadievich Kryzhevich

Saint-Petersburg State University,
Department of Mathematical Physics,
198504, 28, Universitetsky pr, Peterhof, Saint-Petersburg, Russia;
University of Nova Gorica,
Vipavska cesta, 13, Nova Gorica, Slovenia, SI-5000


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.



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