Smooth Attractors Have Zero ‘‘Thickness’’
نویسندگان
چکیده
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 and V. Y. Kaloshin, that the Holder constant of the inverse of a typical linear embedding into ̈ k Ž . R or rank k orthogonal projection can be chosen arbitrarily close to 1 if k is large enough. Q 1999 Academic Press
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