Monotone Flows with Dense Periodic Orbits

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i4.3534

Keywords:

Monotone dynamical systems, Periodic points, Topological transformation groups

Abstract

The main result is Theorem 1: A flow on a connected open set X ⊂ R d is globally periodic provided (i) periodic points are dense in X, and (ii) at all positive times the flow preserves the partial order defined by a closed convex cone that has nonempty interior and contains no straight line. The proof uses the analog for homeomorphisms due to B. Lemmens et al. [27], a classical theorem of D. Montgomery [31, 32], and a sufficient condition for the nonstationary periodic points in a closed order interval to have rationally related periods (Theorem 2).

Author Biography

  • Morris W. Hirsch, University of Wisconsin, Madison
    Department of Mathematics, Honorary Fellow

Downloads

Published

2019-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Monotone Flows with Dense Periodic Orbits. (2019). European Journal of Pure and Applied Mathematics, 12(4), 1350-1359. https://doi.org/10.29020/nybg.ejpam.v12i4.3534

Similar Articles

1-10 of 310

You may also start an advanced similarity search for this article.