On the growth rate inequality for self-maps of the sphere

2023/01/20 by Barge, Héctor, Hernández-Corbato, Luis · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.08543

Abstract

Let S^m = \x₀² + x₁² + ⋯ + x_m² = 1\ and P = \x₀ = x₁ = 0\ ∩ S^m. Suppose that f is a self--map of S^m such that f^-1(P) = P and |deg(f_|P)| < |deg(f)|. Then, the number of fixed points of fⁿ grows at least exponentially with base |d| > 1, where d = deg(f)/deg(f_|P) ∈ \mathbb Z.

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• A survey on the growth rate inequality for sphere endomorphisms

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