The growth rate inequality for Thurston maps with non hyperbolic orbifolds

2022/11/07 by J. Iglesias, Iglesias, J., A. Portela +5 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2211.03571

openalex publication_date 2022/11/07 · openalex created_date 2022/11/13 · openalex updated_date 2026/07/28

Abstract

Let f: S² → S² be a continuous map of degree d, |d|>1, and let N_nf denote the number of fixed points of fⁿ. We show that if f is a Thurston map with non hyperbolic orbifold, then either the growth rate inequality \limsup (1)/(n) log N_nf≥ log |d| holds for f or f has exactly two critical points which are fixed and totally invariant.

Cited by

• A survey on the growth rate inequality for sphere endomorphisms

Related

• On the growth rate inequality for periodic points in the two sphere
• On the growth rate inequality for self-maps of the sphere
• Sphere branched coverings and the growth rate inequality
• A survey on the growth rate inequality for sphere endomorphisms
• Weak expansion properties and large deviation principles for expanding Thurston maps