A survey on the growth rate inequality for sphere endomorphisms

2025/12/22 by Xavier, Juliana
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.19430

Abstract

We survey recent results and current challenges concerning the growth rate inequality for sphere endomorphisms, and present a number of open problems and conjectures arising in this context.

Citations

• Non-locally connected spaces I: Coverings and branched coverings on metric spaces
• Quotients of torus endomorphisms have parabolic orbifolds
• On the growth rate inequality for self-maps of the sphere
• The growth rate inequality for Thurston maps with non hyperbolic orbifolds
• Branched coverings of the sphere having a completely invariant continuum with infinitely many Wada Lakes
• On the growth rate inequality for periodic points in the two sphere
• Sphere branched coverings and the growth rate inequality
• Dynamics of annulus maps III: completeness
• Dynamics of covering maps of the annulus I: semiconjugacies
• Periodic Points and the Measure of Maximal Entropy of an Expanding Thurston Map
• Periodic Points on the 2-sphere
• Classification of expansive attractors on surfaces

Related

• Growth rate for endomorphisms of finitely generated nilpotent groups and solvable groups
• Growth rate of an endomorphism of a group
• Sphere branched coverings and the growth rate inequality
• On the growth rate inequality for periodic points in the two sphere
• On the growth rate inequality for self-maps of the sphere