On the growth rate inequality for periodic points in the two sphere

2017/07/19 by Gerardo Honorato, Honorato, G., J. A. Sabater Iglesias +9 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1707.06144

openalex publication_date 2017/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f:S²→ S² be a continuous map such that deg f = d, |d|>1. Suppose f has two attracting fixed points denoted N and S and let A=S²∖ \N,S\. Assume that if a loop γ⊂ f^-1(A) is homotopically trivial in A, then f(γ) is also homotopically trivial in A. Then, for all n, f has at least |dⁿ -1| fixed points.

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