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

[摘要] We prove that the stable holonomies of a proper codimension 1 attractor Lambda, for a C-r diffeomorphism f of a surface, are not C1+theta for theta greater than the Hausdorff dimension of the stable leaves of f intersected with Lambda. 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. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15