Monotone Flows with Dense Periodic Orbits
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i4.3534Keywords:
Monotone dynamical systems, Periodic points, Topological transformation groupsAbstract
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).Downloads
Published
2019-10-31
Issue
Section
Nonlinear Analysis
License
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.
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