Sets of Invariant Measures and Cesaro Stability
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.
2017
2017-09-30 11:45:03
1033
ergodic theory, invariant measures, shadowing, stability, tolerance stability, topological dynamics
r6
Sergey
Kryzhevich
70
COBISS_ID
3
4924923
NUK URN
18
URN:SI:UNG:REP:CGPCG6IR
cesaro_stability.pdf
542222
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2017-09-30 11:45:12