Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors

Abstract

In this paper, we show that geometric Lorenz attractors have Hausdorff dimension strictly greater than $2$. We use this result to show that for a "large" set of real functions the Lagrange and Markov Dynamical spectrum associated to these attractors has persistently non-empty interior.

22 pages, 6 figures, Accepted by Bulletin of the American Mathematical Society