Diabolical entropy
Dynamical Systems
2019-03-12 v1
Abstract
Milnor and Thurston's famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is H\"older continuous. We obtain a precise formula for the H\"older 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.
Keywords
Cite
@article{arxiv.1610.02563,
title = {Diabolical entropy},
author = {Neil Dobbs and Nicolae Mihalache},
journal= {arXiv preprint arXiv:1610.02563},
year = {2019}
}