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arXiv · 2205.07225

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

Yihan Wang
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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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Yihan Wang. 2022-05-15. On an existence problem of periodic points in intervals whose images cover themselves. https://arxiv.org/abs/2205.07225

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