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Weak forms of shadowing in topological dynamics
Sergey Kryzhevich, Danila Cherkashin, 2017, izvirni znanstveni članek

Opis: We consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomorphisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing) implies possibility to calculate minimal points of the dynamical system. We prove that for the non-wandering case multishadowing is equivalent to density of minimal points. Moreover, it is equivalent to existence of a family of $\varepsilon$-networks ($\varepsilon > 0$) whose iterations are also $\varepsilon$-networks. Relations between multishadowing and some ergodic and topological properties of dynamical systems are discussed.
Najdeno v: ključnih besedah
Ključne besede: Topological dynamics, minimal points, invariant measure, shadowing, chain recurrence, $\varepsilon$-networks, syndetic sets
Objavljeno: 27.07.2017; Ogledov: 2823; Prenosov: 0
.pdf Polno besedilo (499,38 KB)

Sets of Invariant Measures and Cesaro Stability
Sergey Kryzhevich, 2017, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...theory, invariant measures, shadowing, stability, tolerance stability, topological dynamics...
Ključne besede: ergodic theory, invariant measures, shadowing, stability, tolerance stability, topological dynamics
Objavljeno: 02.10.2017; Ogledov: 2200; Prenosov: 0
.pdf Polno besedilo (529,51 KB)

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