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Transactions of the Moscow Mathematical Society

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


Author: N. A. Solodovnikov
Translated by: Christopher Hollings
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2014, 69-76
MSC (2010): Primary 37E99
DOI: https://doi.org/10.1090/S0077-1554-2014-00241-7
Published electronically: November 6, 2014
MathSciNet review: 3308600
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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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Additional Information

N. A. Solodovnikov
Affiliation: National Research University “Higher School of Economics”, Moscow
Email: proba-f@va.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00241-7
Keywords: Attractor, intermingling basins, Ittai Kan diffeomorphism
Published electronically: November 6, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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