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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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 |
|---|---|
| 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: | Date Event 15 December 2007 Published |
| 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 |
| URI: | https://wrap.warwick.ac.uk/30754/ |
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