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arXiv · 1712.09223

Monotone dynamical systems with dense periodic points

Bas Lemmens·Onno van Gaans·Hent van Imhoff
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Abstract

In this paper we prove a recent conjecture by M. Hirsch, which says that if $(f,\Omega)$ is a discrete time monotone dynamical system, with $f\colon \Omega\to\Omega$ a homeomorphism on an open connected subset of a finite dimensional vector space, and the periodic points of $f$ are dense in $\Omega$, then $f$ is periodic.

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Bas Lemmens, Onno van Gaans, Hent van Imhoff. 2017-12-26. Monotone dynamical systems with dense periodic points. https://arxiv.org/abs/1712.09223

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