Work

On invariant measures of ‘satellite’ infinitely renormalizable quadratic polynomials

Year: 2024

Type: article

Abstract: Let $f(z)=z^2+c$ be an infinitely renormalizable quadratic polynomial and $J_\infty $ be the intersection of forward orbits of ‘small’ Julia sets of its simple renormalizations. We prove that if f admits an infinite sequence of satellite renormalizations, then every invariant measure of $f: J_\infty \to J_\infty $ is supported on the postcritical set and has zero Lyapunov exponent. Coupled with [13], this implies that the Lyapunov exponent of such f at c is equal to zero, which partly answers a question posed by Weixiao Shen.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2024.85

Authors: GENADI LEVIN, FELIKS PRZYTYCKI

Institutions: Hebrew University of Jerusalem, Institute of Mathematics, Polish Academy of Sciences

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: Narodowym Centrum Nauki