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Cantor exchange systems and renormalization
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Pinto, A. A., Rand, D. A. (David A.) and Feffeira, F. (2007) Cantor exchange systems and renormalization. Journal of Differential Equations, Vol.243 (No.2). pp. 593-616. doi:10.1016/j.jde.2007.09.014 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2007.09.014
Abstract
We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Differential Equations | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-0396 | ||||
Official Date: | 15 December 2007 | ||||
Dates: |
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Volume: | Vol.243 | ||||
Number: | No.2 | ||||
Number of Pages: | 24 | ||||
Page Range: | pp. 593-616 | ||||
DOI: | 10.1016/j.jde.2007.09.014 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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