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Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
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Orientador(es)
Resumo(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.
Descrição
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Contexto Educativo
Citação
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
Editora
Academic Press Inc. Elsevier Science