Poisson stable motions of monotone nonautonomous dynamical systems
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CHEBAN, David, LIU, Zhenxin. Poisson stable motions of monotone nonautonomous dynamical systems. In: Science China Mathematics, 2019, nr. 7(62), pp. 1391-1418. ISSN 1674-7283. DOI: https://doi.org/10.1007/s11425-018-9407-8
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Science China Mathematics
Numărul 7(62) / 2019 / ISSN 1674-7283

Poisson stable motions of monotone nonautonomous dynamical systems

DOI: https://doi.org/10.1007/s11425-018-9407-8

Pag. 1391-1418

Cheban David1, Liu Zhenxin2
 
1 Necunoscută, China,
2 School of Mathematical Sciences, Dalian University of Technology
 
Disponibil în IBN: 31 octombrie 2019


Rezumat

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. 

Cuvinte-cheie
almost automorphy, Bohr/Levitan almost periodicity, comparability, monotone nonautonomous dynamical systems, periodicity, Poisson stability, quasi-periodicity, topological dynamics