Monotone dynamical systems with dense periodic points

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Abstract

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

MSC

primary
37C25
secondary
47H07

Keywords

Chaos
Dense periodic points
Monotone dynamical systems

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