9,678 research outputs found
Non-uniformly hyperbolic horseshoes in the standard family
We show that the non-uniformly hyperbolic horseshoes of Palis and Yoccoz
occur in the standard family of area-preserving diffeomorphisms of the
two-torus for a set of (large) parameters of positive Lebesgue measure
A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets
In 1954 Marstrand proved that if K is a subset of R^2 with Hausdorff
dimension greater than 1, then its one-dimensional projection has positive
Lebesgue measure for almost-all directions. In this article, we give a
combinatorial proof of this theorem when K is the product of regular Cantor
sets of class C^{1+a}, a>0, for which the sum of their Hausdorff dimension is
greater than 1.Comment: 9 pages, 1 figure, referee suggestions incorporated, to appear in
Expositiones Mathematica
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