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arXiv · 2003.00548

A Riemannian metric on polynomial hyperbolic components

Yan Mary He·Hongming Nie
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Abstract

We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree $d \ge 2$ 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.

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Yan Mary He, Hongming Nie. 2020-03-01. A Riemannian metric on polynomial hyperbolic components. https://arxiv.org/abs/2003.00548

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