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Indexed by:Journal Papers

Date of Publication:2019-07-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:62

Issue:7

Page Number:1391-1418

ISSN No.:1674-7283

Key Words:topological dynamics; comparability; periodicity; quasi-periodicity; Bohr; Levitan almost periodicity; almost automorphy; Poisson stability; monotone nonautonomous dynamical systems

Abstract:In this paper, we study the Poisson stability (in particular, stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, Poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations (ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned Poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.