Poisson stable motions of monotone nonautonomous dynamical systems  

作　　者：David Cheban Zhenxin Liu 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China [2]Department of Mathematics, Faculty of Mathematics and Informatics, State University of Moldova, Chisinau AfD-2009, Moldova

出　　处：《Science China Mathematics》2019年第7期1391-1418,共28页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11271151 and 11522104);the Startup and Xinghai Jieqing Funds from Dalian University of Technology

摘　　要：In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, 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.In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, 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.

关 键 词：topological dynamics comparability PERIODICITY QUASI-PERIODICITY Bohr/Levitan ALMOST PERIODICITY ALMOST automorphy POISSON stability MONOTONE nonautonomous dynamical systems 

分 类 号：O1[理学—数学]