Monotone dynamical systems with dense periodic points

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Lemmens, Bas¹  van Gaans, Onno²  van Imhoff, Hent² 

[1] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury CT2 7NX, Kent, England

[2] Leiden Univ, Math Inst, POB 9512, NL-2300 RA Leiden, Netherlands

关键词: Chaos;    Dense periodic points;    Monotone dynamical systems;   

DOI  :  10.1016/j.jde.2018.07.012

来源: Elsevier

【 摘 要 】

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: Omega -> 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free