Cantor exchange systems and renormalization
We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely co...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2007
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| Texto completo: | https://hdl.handle.net/10216/93226 |
| País: | Portugal |
| Oai: | oai:repositorio-aberto.up.pt:10216/93226 |
| Resumo: | We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set. (C) 2007 Published by Elsevier Inc. |
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