Stable sets, hyperbolicity and dimension
Abstract
In this note we derive an upper bound for the Hausdorff dimension of the stable set of a hyperbolic set of a C2 diffeomorphisms on a n-dimensional manifold. As a consequence we obtain that H Ws()=n is equivalent to the existence of a SRB-measure. We also discuss related results in the case of expanding maps.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.