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

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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}

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

V. A. Kleptsyn^a, P. S. Saltykov^b

^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}

$C^2$ -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

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\by V.~A.~Kleptsyn, P.~S.~Saltykov

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

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\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.

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\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}

Linking options:

https://www.mathnet.ru/eng/mmo18

https://www.mathnet.ru/eng/mmo/v72/i2/p249

This publication is cited in the following 8 articles:

Nunez-Madariaga B., Ramirez S.A., Vasquez C.H., “Measures Maximizing the Entropy For Kan Endomorphisms”, Nonlinearity, 34:10 (2021), 7255–7302
Bonatti Ch., Minkov S., Okunev A., Shilin I., “Anosov Diffeomorphism With a Horseshoe That Attracts Almost Any Point”, Discret. Contin. Dyn. Syst., 40:1 (2020), 441–465
Gan Sh., Shi Y., “Robustly Topological Mixing of Kan'S Map”, J. Differ. Equ., 266:11 (2019), 7173–7196
Cheng Ch., Gan Sh., Shi Y., “A Robustly Transitive Diffeomorphism of Kan'S Type”, Discret. Contin. Dyn. Syst., 38:2 (2018), 867–888
Ures R., Vasquez C.H., “On the Non-Robustness of Intermingled Basins”, Ergod. Theory Dyn. Syst., 38:1 (2018), 384–400
Gharaei M., Homburg A.J., “Random Interval Diffeomorphisms”, Discret. Contin. Dyn. Syst.-Ser. S, 10:2 (2017), 241–272
N. A. Solodovnikov, “Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open”, Trans. Moscow Math. Soc., 75 (2014), 69–76
Kleptsyn V., Ryzhov D., Minkov S., “Special Ergodic Theorems and Dynamical Large Deviations”, Nonlinearity, 25:11 (2012), 3189–3196

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Moskovskogo Matematicheskogo Obshchestva

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