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Smooth attractors have zero "thickness"
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UNSPECIFIED (1999) Smooth attractors have zero "thickness". JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 240 (1). pp. 37-46. ISSN 0022-247X.
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Abstract
A finite-dimensional global attractor A can be embedded, using some linear map L, into a Euclidean space R-k of sufficiently high dimension. The Holder exponent of L-1 depends upon k and upon tau(A), the "thickness exponent" of A. We show that global attractors which are uniformly bounded in the Sobolev spaces H-s for all s > 0 have tau(A = 0. It follows, using a result of B. R. Hunt and V. Y. Kaloshin, that the Holder constant of the inverse of a typical linear embedding into R-k (or rank k orthogonal projection) can be chosen arbitrarily close to 1 if k is large enough. (C) 1999 Academic Press.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | ||||
Publisher: | ACADEMIC PRESS INC | ||||
ISSN: | 0022-247X | ||||
Official Date: | 1 December 1999 | ||||
Dates: |
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Volume: | 240 | ||||
Number: | 1 | ||||
Number of Pages: | 10 | ||||
Page Range: | pp. 37-46 | ||||
Publication Status: | Published |
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