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- W2020295960 abstract "We prove a one-to-one correspondence between (i) C 1 + conjugacy classes of C 1 + H Cantor exchange systems that are C 1 + H fixed points of renormalization and (ii) C 1 + conjugacy classes of C 1 + H diffeomorphisms f with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ . However, we prove that there is no C 1 + α Cantor exchange system, with bounded geometry, that is a C 1 + α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set." @default.
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- W2020295960 date "2007-12-01" @default.
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- W2020295960 title "Cantor exchange systems and renormalization" @default.
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