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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 homeomor- phisms 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 exis- tence of a family of ε-networks (ε > 0) whose iterations are also ε-networks. Relations between multishadowing and some ergodic and topological properties of dynamical systems are discussed.
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Authors (2)
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Danila Cherkashin Ph.D.
- Saint Petersburg State University
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Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.12775/TMNA.2017.020
- License
- Copyright (2017 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
Topological Methods in Nonlinear Analysis
no. 50,
pages 125 - 150,
ISSN: 1230-3429 - Language:
- English
- Publication year:
- 2017
- Bibliographic description:
- Cherkashin D., Kryzhevich S.: Weak forms of shadowing in topological dynamics// Topological Methods in Nonlinear Analysis -,iss. 1 (2017), s.125-150
- DOI:
- Digital Object Identifier (open in new tab) 10.12775/tmna.2017.020
- Sources of funding:
-
- Free publication
- Verified by:
- Gdańsk University of Technology
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