Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
For the real quadratic map and a given a point has good expansion properties if any interval containing also contains a neighborhood of with univalent, with bounded distortion and for some . The -weakly expanding set is the set of points which do not have good expansion properties. Let denote the negative fixed point and the first return time of the critical orbit to . We show there is a set of parameters with positive Lebesgue measure for which the Hausdorff dimension of...
Let , , and let be a continuous map having the branching point fixed. We prove that is distributionally chaotic iff the topological entropy of is positive.
We continue our study of the dynamics of mappings with small topological degree on projective complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic “equilibrium” measure for each such mapping. Here we study the dynamical properties of this measure in detail: we give optimal bounds for its Lyapunov exponents, prove that it has maximal entropy, and show that it has product structure in the natural extension. Under a natural further assumption, we show that saddle points...