Global phase space universality, smooth conjugacies and renormalisation: I. The C1+alpha case
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 0951-7715Full text not available from this repository.
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|
|Number of Pages:||22|
|Page Range:||pp. 181-202|
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