A Riemannian metric on polynomial hyperbolic components
Dynamical Systems
2020-03-03 v1
Abstract
We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree polynomials. Our metric is constructed by considering the measure-theoretic entropy of a polynomial with respect to some equilibrium state. As applications, we show that the Hausdorff dimension function has no local maximum on such hyperbolic components. We also give a sufficient condition for a point not being a critical point of the Hausdorff dimension function.
Cite
@article{arxiv.2003.00548,
title = {A Riemannian metric on polynomial hyperbolic components},
author = {Yan Mary He and Hongming Nie},
journal= {arXiv preprint arXiv:2003.00548},
year = {2020}
}