On an existence problem of periodic points in intervals whose images cover themselves

2022/05/15 by Yihan Wang, Wang, Yihan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #math.CO #math.DS

paper · pdf · doi:10.48550/arxiv.2205.07225

11 pages

arxiv created 2022/05/15 · openalex publication_date 2022/05/15 · arxiv updated 2022/05/17 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

We consider k intervals on the real line whose images under a continuous map f contain themselves. It's conjectured that there exists a periodic point of period not bigger than k in these intervals. We prove the conjecture for k=5 in this paper. We also propose a discretization method in attempt to solve the problem.

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