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Advisor(s)
Abstract(s)
There 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.
Description
Keywords
Hyperbolic systems Attractors Hausdorff dimension
Citation
Publisher
Birkhäuser Basel