Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open
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N. A. Solodovnikov
Translated by: Christopher Hollings - Trans. Moscow Math. Soc. 2014, 69-76
- DOI: https://doi.org/10.1090/S0077-1554-2014-00241-7
- Published electronically: November 6, 2014
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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.References
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Bibliographic Information
- N. A. Solodovnikov
- Affiliation: National Research University “Higher School of Economics”, Moscow
- Email: proba-f@va.ru
- Published electronically: November 6, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2014, 69-76
- MSC (2010): Primary 37E99
- DOI: https://doi.org/10.1090/S0077-1554-2014-00241-7
- MathSciNet review: 3308600