Diabolical entropy

Abstract

Milnor and Thurston's famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is Hölder continuous. We obtain a precise formula for the Hölder exponent at almost every quadratic parameter. Furthermore, the entropy of most parameters is proven to be in a set of Hausdorff dimension smaller than one, while most values of the entropy arise from a set of parameters of dimension smaller than one.

References in corpus (4)

• Core entropy of quadratic polymonials
• Geometric pressure for multimodal maps of the interval
• Statistical properties of unimodal maps: physical measures, periodic orbits and pathological laminations
• Free energy and equilibrium states for families of interval maps

Cited by in corpus (2)

• Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters
• On fair entropy of the tent family