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 Tr. Mosk. Mat. Obs., 2014, Volume 75, Issue 1, Pages 15–24 (Mi mmo555)

Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open

N. A. Solodovnikov

National Research University "Higher School of Economics", Moscow

Abstract: We construct an open set of $C^2$-diffeomorphisms which preserve the boundary of some manifold, and which have the following property: for each mapping, the basin of attraction of one component of the attractor is open and everywhere dense, but the basin of attraction of the second component is nowhere dense, though its measure is positive.

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English version:
Transactions of the Moscow Mathematical Society, 2014, 75, 69–76

Document Type: Article
UDC: 517.938.5
MSC: 37E99

Citation: N. A. Solodovnikov, “Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open”, Tr. Mosk. Mat. Obs., 75, no. 1, MCCME, M., 2014, 15–24; Trans. Moscow Math. Soc., 75 (2014), 69–76

Citation in format AMSBIB
\Bibitem{Sol14} \by N.~A.~Solodovnikov \paper Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open \serial Tr. Mosk. Mat. Obs. \yr 2014 \vol 75 \issue 1 \pages 15--24 \publ MCCME \publaddr M. \mathnet{http://mi.mathnet.ru/mmo555} \elib{http://elibrary.ru/item.asp?id=23780152} \transl \jour Trans. Moscow Math. Soc. \yr 2014 \vol 75 \pages 69--76 \crossref{https://doi.org/10.1090/S0077-1554-2014-00241-7} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960131684}