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A C-infinity Diffeomorphism with Infinitely Many Intermingled Basins

Melbourne, I and Windsor, A (2005) A C-infinity Diffeomorphism with Infinitely Many Intermingled Basins Ergodic Theory and Dynamical Systems, 25 (06).


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Let M be the four-dimensional compact manifold M = T-2 x S-2 and let k >= 2. We construct a C-infinity diffeomorphism F : M -> M with precisely k intermingled minimal attractors A(1),...,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 -> M with a countable infinity of intermingled minimal attractors.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Windsor, A
Date : 1 January 2005
DOI : 10.1017/S0143385705000325
Additional Information : Published in <i>Ergodic Theory and Dynamical Systems,</i> Vol. 25, Pt. 6. Copyright 2005 Cambridge University Press. Click <a href=>here</a> to access the journal's website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:06
Last Modified : 31 Oct 2017 13:57

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