Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

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

http://hdl.handle.net/10400.22/6654

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Authors

Pinto, Alberto A.

Rand, David A.

Ferreira, Flávio

Abstract(s)

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

URI

http://hdl.handle.net/10400.22/6654

Citation

Pinto, A. A., Rand, D. A., & Ferreira, E. (2007). Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Journal of Differential Equations, 243(2), 168–178. DOI: 10.1016/j.jde.2007.02.013

Publisher

Academic Press Inc. Elsevier Science

DOI

10.1016/j.jde.2007.02.013

Collections

ESEIG - MAT - Artigos

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cclicense-by-nc-nd

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