Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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F. Bianchi - Y. M. He

Pressure path metrics on parabolic families of polynomials

created by bianchi on 23 Sep 2024

[BibTeX]

preprint

Inserted: 23 sep 2024
Last Updated: 23 sep 2024

Year: 2024

ArXiv: 2409.10462 PDF

Abstract:

Let $\Lambda$ be a subfamily of the moduli space of degree $D\ge2$ polynomials defined by a finite number of parabolic relations. Let $\Omega$ be a bounded stable component of $\Lambda$ with the property that all critical points are attracted by either the persistent parabolic cycles or by attracting cycles in $\mathbb C$. We construct a positive semi-definite pressure form on $\Omega$ and show that it defines a path metric on $\Omega$. This provides a counterpart in complex dynamics of the pressure metric on cusped Hitchin components recently studied by Kao and Bray-Canary-Kao-Martone.

Tags: PRIN2022-MFDS

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