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Global phase space universality, smooth conjugacies and renormalisation: I. The C1+alpha case
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Rand, D. A. (David A.). (1988) Global phase space universality, smooth conjugacies and renormalisation: I. The C1+alpha case. NONLINEARITY, 1 (1). pp. 181-202. ISSN 0951-7715
Full text not available from this repository.Abstract
Previous results about universality in phase space have been local in nature and only concern scaling about a single point. In this paper I prove that a much stronger global result holds for three important examples: period-doubling cascades, golden critical circle maps and certain diffeomorphisms of the circle. In each case I prove that the conjugacy between the appropriate phase space structures of two systems in the same stable manifold of the appropriate renormalisation transformation is or can be extended to a C1+alpha diffeomorphism. This means that the structures are globally geometrically equivalent and have the same global quantitative scaling properties. These results are corollaries of a general theory for Markov families and the general techniques and results should be applicable to a much wider class of problems.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
| Journal or Publication Title: | NONLINEARITY |
| Publisher: | IOP PUBLISHING LTD |
| ISSN: | 0951-7715 |
| Date: | February 1988 |
| Volume: | 1 |
| Number: | 1 |
| Number of Pages: | 22 |
| Page Range: | pp. 181-202 |
| Publication Status: | Published |
| Funder: | SERC |
| URI: | http://wrap.warwick.ac.uk/id/eprint/24617 |
Data sourced from Thomson Reuters' Web of Knowledge
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