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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. doi:10.1088/0951-7715/1/1/007 ISSN 0951-7715.
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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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | February 1988 | ||||
Dates: |
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Volume: | 1 | ||||
Number: | 1 | ||||
Number of Pages: | 22 | ||||
Page Range: | pp. 181-202 | ||||
DOI: | 10.1088/0951-7715/1/1/007 | ||||
Publication Status: | Published | ||||
Funder: | SERC |
Data sourced from Thomson Reuters' Web of Knowledge
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