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
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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