Mathematical Research Letters

Volume 30 (2023)

Number 3

A Riemannian metric on hyperbolic components

Pages: 733 – 764

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n3.a6

Authors

Yan Mary He (Department of Mathematics, University of Oklahoma, Norman, Ok., U.S.A.)

Hongming Nie (Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York, U.S.A.)

Abstract

We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree at least $2$ rational maps in one complex variable. Our metric is constructed by considering the measure-theoretic entropy of a rational map with respect to some equilibrium state.

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The second author was partially supported by ISF Grant 1226/17 and by CONICYT PIA ACT172001.

Received 3 April 2020

Received revised 16 September 2022

Accepted 17 December 2022

Published 15 December 2023