Chain transitive sets for smooth strongly monotone dynamical systems
Dynamical Systems
2012-04-10 v1
Abstract
Let K denote a compact invariant set for a strongly monotone semiflow in an ordered Banach space E, satisfying standard smoothness and compactness assumptions. Suppose the semiflow restricted to K is chain transitive. The main result is that either K is unordered, or else K is contained in totally ordered, compact arc of stationary points; and the latter cannot occur if the semiflow is real analytic and dissipative. As an application, entropy is 0 when E = R^3 . Analogous results are proved for maps. The main tools are results of Mierczynski [27 ] and Terescak [37 ]
Cite
@article{arxiv.1204.1703,
title = {Chain transitive sets for smooth strongly monotone dynamical systems},
author = {Morris W. Hirsch},
journal= {arXiv preprint arXiv:1204.1703},
year = {2012}
}
Comments
Published in Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 5, 1999, 529-543