On C^2-stable effects of intermingled basins of attractors in classes of boundary-preserving maps

Namely, the attraction basins of each of the boundary components are everywhere dense in the phase space for such maps. Moreover, the Hausdorff dimension of the set of points that are not attracted by either of the components proves to be less than the dimension of the phase space itself, which stre...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of the Moscow Mathematical Society 2011, Vol.72, p.193-217
Main Authors: Kleptsyn, Victor A., Saltykov, Petr S.
Format: Article
Language:English
Subjects:
Dynamical Systems
Mathematics
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Namely, the attraction basins of each of the boundary components are everywhere dense in the phase space for such maps. Moreover, the Hausdorff dimension of the set of points that are not attracted by either of the components proves to be less than the dimension of the phase space itself, which strengthens the result following from the argument due to Bonatti, Diaz, and Viana.]]>
ISSN:0077-1554
1547-738X
DOI:10.1090/S0077-1554-2012-00196-4