We study the Hausdorff dimension for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topological entropy.
Abstract. In this paper we study the radial and orthogonal projections and the distance sets of the random Cantor sets E ⊂ R 2 which are called Mandelbrot percolation or percolation fractals. We prove that the following assertion holds almost surely: if the Hausdorff dimension of E is greater than 1 then the orthogonal projection to every line, the radial projection with every center, and distance set from every point contain intervals.
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