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Trudy Moskovskogo Matematicheskogo Obshchestva, 2011, Volume 72, Issue 2, Pages 249–280 (Mi mmo18)  
This article is cited in 8 scientific papers (total in 8 papers)

On $C^2$-stable effects of intermingled basins of attractors in classes of boundary-preserving maps

V. A. Kleptsyna, P. S. Saltykovb

a CNRS, Institut de Recherche Mathématique de Rennes (UMR 6625)
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (361 kB) Citations (8)
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Abstract: In the spaces of boundary-preserving maps of an annulus and a thickened torus, we construct open sets in which every map has intermingled basins of attraction, as predicted by I. Kan.
Namely, the attraction basins of each of the boundary components are everywhere dense in the phase space for such maps. Moreover, the Hausdorff dimension of the set of points that are not attracted by either of the components proves to be less than the dimension of the phase space itself, which strengthens the result following from the argument due to Bonatti, Diaz, and Viana.
Key words and phrases: dynamical system, attractor, stability, partially hyperbolic skew product, Hцlder rectifying map.
Received: 22.03.2011
English version:
Transactions of the Moscow Mathematical Society, 2011, Volume 72, Pages 193–217
DOI: https://doi.org/10.1090/S0077-1554-2012-00196-4
Bibliographic databases:
Document Type: Article
UDC: 517.987.5+517.938.5
MSC: 37C70, 37D25
Language: Russian
Citation: V. A. Kleptsyn, P. S. Saltykov, “On $C^2$-stable effects of intermingled basins of attractors in classes of boundary-preserving maps”, Tr. Mosk. Mat. Obs., 72, no. 2, MCCME, Moscow, 2011, 249–280; Trans. Moscow Math. Soc., 72 (2011), 193–217
Citation in format AMSBIB
\Bibitem{KleSal11}
\by V.~A.~Kleptsyn, P.~S.~Saltykov
\paper On $C^2$-stable effects of intermingled basins of attractors in classes of boundary-preserving maps
\serial Tr. Mosk. Mat. Obs.
\yr 2011
\vol 72
\issue 2
\pages 249--280
\publ MCCME
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/mmo18}
\zmath{https://zbmath.org/?q=an:06026278}
\elib{https://elibrary.ru/item.asp?id=21369344}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2011
\vol 72
\pages 193--217
\crossref{https://doi.org/10.1090/S0077-1554-2012-00196-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84868114456}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Trudy Moskovskogo Matematicheskogo Obshchestva
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