Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
| Data(s) |
08/10/2015
08/10/2015
2007
|
|---|---|
| Resumo |
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. |
| Identificador |
10.1016/j.jde.2007.02.013 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 http://hdl.handle.net/10400.22/6654 10.1016/j.jde.2007.02.013 0022-0396 |
| Idioma(s) |
eng |
| Publicador |
Academic Press Inc. Elsevier Science |
| Direitos |
openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Tipo |
article |
