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A C^\infty diffeomorphism with infinitely many intermingled basins

Melbourne, Ian and Windsor, A. (2005) A C^\infty diffeomorphism with infinitely many intermingled basins Dynamical Systems.


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Let M be the four-dimensional compact manifold M = T2 times S2 and let k greater than or equal to 2. We construct a C^\infty diffeomorphism F: M to M with precisely k intermingled minimal attractors A1,..., Ak. Moreover the union of the basins is a set of full Lebesgue measure. This means that Lebesgue almost every point in M lies in the basin of attraction of Aj for some j, but every non-empty open set in M has a positive measure intersection with each basin. We also construct F:M to M with a countable infinity of intermingled minimal attractors.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Windsor, A.
Date : 15 September 2005
Additional Information : Published online September 2005 in Ergodic Theory and Dynamical Systems. Issue and page numbers to be provided once the paper edition is published. © 2005 Cambridge University Press. Reprinted with permission.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 31 Oct 2017 14:01

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