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Title:Weak forms of shadowing in topological dynamics
Authors:ID Kryzhevich, Sergey, University of Nova Gorica (Author)
ID Cherkashin, Danila, Saint-Petersburg State University (Author), et al.
Files: This document has no files that are freely available to the public. This document may have a physical copy in the library of the organization, check the status via COBISS. Link is opened in a new window
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
Abstract: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.
Keywords:Topological dynamics, minimal points, invariant measure, shadowing, chain recurrence, $\varepsilon$-networks, syndetic sets
Publication version:Author Accepted Manuscript
Year of publishing:2017
Number of pages:26
Numbering:online first
PID:20.500.12556/RUNG-3185-7d83ccb7-bc05-c046-8a6c-5cec326badb3 New window
COBISS.SI-ID:4868859 New window
DOI:http://dx.doi.org/10.12775/TMNA.2017.020 New window
NUK URN:URN:SI:UNG:REP:6HPH6AQ7
Publication date in RUNG:27.07.2017
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Record is a part of a journal

Title:Topological Methods in Nonlinear Analysis
Publisher:Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies
Year of publishing:2017
ISSN:1230-3429

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