Cantor exchange systems and renormalization

Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio

http://hdl.handle.net/10400.22/6656

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Authors

Pinto, Alberto A.

Rand, David A.

Ferreira, Flávio

Abstract(s)

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.

URI

http://hdl.handle.net/10400.22/6656

Citation

Pinto, A. A., Rand, D. A., & Feffeira, F. (2007). Cantor exchange systems and renormalization. Journal of Differential Equations, 243(2), 593–616. DOI: 10.1016/j.jde.2007.09.014