Monotone dynamical systems with dense periodic points

Bas Lemmens; Onno van Gaans; Hent van Imhoff

Monotone dynamical systems with dense periodic points

Dynamical Systems 2017-12-27 v1 Optimization and Control

Authors: Bas Lemmens , Onno van Gaans , Hent van Imhoff

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.

Keywords

dynamical systems and chaos periodic orbits in hamiltonian systems holomorphic dynamics

Cite

@article{arxiv.1712.09223,
  title  = {Monotone dynamical systems with dense periodic points},
  author = {Bas Lemmens and Onno van Gaans and Hent van Imhoff},
  journal= {arXiv preprint arXiv:1712.09223},
  year   = {2017}
}

Comments

5 pages

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