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EXISTENCE, NONEXISTENCE AND UNIVERSAL BREAKDOWN OF DISSIPATIVE GOLDEN INVARIANT TORI .2. CONVERGENCE OF RENORMALIZATION FOR MAPPINGS OF THE ANNULUS
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UNSPECIFIED (1992) EXISTENCE, NONEXISTENCE AND UNIVERSAL BREAKDOWN OF DISSIPATIVE GOLDEN INVARIANT TORI .2. CONVERGENCE OF RENORMALIZATION FOR MAPPINGS OF THE ANNULUS. NONLINEARITY, 5 (3). pp. 663-680. ISSN 0951-7715.
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Abstract
In this series of three papers I rigorously formulate and prove a number of the main conjectures associated with renormalization of golden-mean quasi-periodic dynamical systems. In particular, in the previous paper, I proved the existence of an open set of families of analytic mappings of the circle with the universal properties described in earlier papers. In this paper, I extend this to dissipative annulus mappings and study the definition and convergence of renormalization operators for higher-dimensional systems. In the sequel I formulate and prove general results about when convergence of renormalization implies existence of an invariant circle and then describe part of the boundary of the set of dissipative diffeomorphisms of the annulus and its universal structure.
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: | May 1992 | ||||
Dates: |
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Volume: | 5 | ||||
Number: | 3 | ||||
Number of Pages: | 18 | ||||
Page Range: | pp. 663-680 | ||||
Publication Status: | Published |
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