Monotone flows with dense periodic orbits
- Author(s): Hirsch, MW
- et al.
Published Web Locationhttps://doi.org/10.29020/nybg.ejpam.v12i4.3534
© 2019 EJPAM. The main result is Theorem 1: A flow on a connected open set X ⊂ Rd 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. , 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).