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Smooth Attractors Have Zero ‘‘Thickness’’
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 ̈ y1 Ž . of L depends upon k and upon t A , the ‘‘thickness exponent’’ of A. We show that global attractors which are uniformly bounded in the Sobolev spaces H s for Ž . all s ) 0 have t A s 0. It follows, using a result of B. R. Hunt an...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1999
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6569