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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Abstract

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,..., A_k. 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 A_j 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 :	Name Email ORCID Melbourne, Ian i.melbourne@surrey.ac.uk 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
URI:	http://epubs.surrey.ac.uk/id/eprint/1452

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