Ferreira, FlávioPinto, Alberto A.Rand, David A.2015-12-022015-12-022007978-3-7643-8481-4978-3-7643-8482-1http://hdl.handle.net/10400.22/7045There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.engHyperbolic systemsAttractorsHausdorff dimensionbook part10.1007/978-3-7643-8482-1_15