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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 3, Pages 505–520
DOI: https://doi.org/10.4213/tmf10033
(Mi tmf10033)
 

This article is cited in 1 scientific paper (total in 1 paper)

Nonwandering continuum possessing the Wada property

D. W. Serow

State Institute of Economy, Finance, Law, and Technology, Gatchina, Russia
References:
Abstract: Dynamic systems acting on the plane and possessing the Wada property have been observed. There exist only two topological types, symmetric and antisymmetric, of dissipative dynamic systems with the nonwandering continuum being a common boundary of three regions. An antisymmetric dynamic system with the nonwandering continuum can be transformed into a dynamic system with an invariant vortex street without fixed points. A further factorization procedure allows obtaining a dynamic system having the Wada property with the nonwandering continuum being a common boundary of any finite number of regions. Moreover, following this strategy, it is possible to construct a Birkhoff curve that is a common boundary of two regions (problem $1100$).
Keywords: dynamic system, Wada basin, Wada property, Birkhoff curve, indecomposable continuum (atom), composant, nonwandering set, rotation number, Schnirelmann density, PostScript.
Received: 14.12.2020
Revised: 01.04.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 3, Pages 841–853
DOI: https://doi.org/10.1134/S0040577921060118
Bibliographic databases:
Document Type: Article
PACS: 02.30.Hq; 05.45.-a
Language: Russian
Citation: D. W. Serow, “Nonwandering continuum possessing the Wada property”, TMF, 207:3 (2021), 505–520; Theoret. and Math. Phys., 207:3 (2021), 841–853
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf10033
  • https://doi.org/10.4213/tmf10033
  • https://www.mathnet.ru/eng/tmf/v207/i3/p505
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:76
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