Smooth Attractors Have Zero “Thickness”☆

  title={Smooth Attractors Have Zero “Thickness”☆},
  author={Peter K. Friz and James C. Robinson},
  journal={Journal of Mathematical Analysis and Applications},
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 τ( 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 τ( 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… 
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