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).
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||1 January 2005|
|Identification Number :||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=http://journals.cambridge.org>here</a> to access the journal's website.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:06|
|Last Modified :||23 Sep 2013 18:26|
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