Chain transitive sets for smooth strongly monotone dynamical systems

Details Chain transitive sets for smooth strongly monotone dynamical systems Chain transitive sets for smooth strongly monotone dynamical systems

2012-04-08

arxiv.org/abs/1204.1703v1

Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 5, 1999, 529-543

Mathematics

Dynamical Systems

Published in Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 5, 1999, 529-543

Scientific paper

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 ]

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