Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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Item POISSON STABLE MOTIONS AND GLOBAL ATTRACTORS OF SYMMETRIC MONOTONE NONAUTONOMOUS DYNAMICAL SYSTEMS(2022) Ceban, DavidThis paper is dedicated to the study of the problem of existence of Poisson stable (Bohr/Levitan almost periodic, almost automorphic, almost recurrent, recurrent, pseudo-periodic, pseudo-recurrent and Poisson stable) motions of symmetric monotone non-autonomous dynamical systems (NDS). It is proved that every precompact motion of such system is asymptotically Poisson stable. We give also the description of the structure of compact global attractor for monotone NDS with symmetry. We establish the main results in the framework of general non-autonomous (cocycle) dynamical systems. We apply our general results to the study of the problem of existence of different classes of Poisson stable solutions and global attractors for a chemical reaction network and nonautonomous translation-invariant difference equations.Item DIFFERENT TYPES OF COMPACT GLOBAL ATTRACTORS FOR COCYCLES WITH A NONCOMPACT PHASE SPACE OF DRIVING SYSTEM AND THE RELATIONSHIP BETWEEN THEM(2022) Ceban, DavidIn this paper we study different types of compact global attractors for non-autonomous (cocycle) dynamical systems with noncompact phase space of driving system. We establish the relations between them.Item ALMOST PERIODIC AND ALMOST AUTOMORPHIC SOLUTIONS OF MONOTONE DIFFERENTIAL EQUATIONS WITH A STRICT MONOTONE FIRST INTEGRAL(2020) Ceban, DavidThe paper is dedicated to the study of problem of Poisson stability (in particular periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo-recurrence, Poisson stability) and asymptotical Poisson stability of motions of monotone non-autonomous differential equations which admit a strict monotone first integral. This problem is solved in the framework of general non-autonomous dynamical systems.Item LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS AND NONAUTONOMOUS DYNAMICAL SYSTEMS(CEP USM, 2017) Ceban, DavidWe prove that the linear stochastic equation dx(t) = (Ax(t)+f(t))dt+g(t)dW(t) (*) with linear operator A generating a C0-semigroup{U(t)}t≥0 and Levitan almost periodic forcing termsf and g admits a unique Levitan almost periodic [3,ChIV] solution in distrution sense if it has at least one precompact solution on R+and the semigroup{U(t)}t≥0is asymptotically stable.Item ASYMPTOTIC STABILITY OF INFINITE-DIMENSIONAL NONAUTONOMOUS DYNAMICAL SYSTEMS(Academy of Sciences of Moldova, 2013) Ceban, DavidThis paper is dedicated to the study of the problem of asymptotic stabil- ity for general non-autonomous dynamical systems (both with continuous and discrete time). We study the relation between diÆerent types of attractions and asymptotic stability in the framework of general non-autonomous dynamical systems. Specially we investigate the case of almost periodic systems, i.e., when the base (driving sys- tem) is almost periodic. We apply the obtained results we apply to diÆerent classes of non-autonomous evolution equations: Ordinary DiÆerential Equations, Functional DiÆerential Equations (both with Ønite retard and neutral type) and Semi-Linear Parabolic EquationsItem RELATION BETWEEN LEVINSON CENTER, CHAIN RECURRENT SET AND CENTER OF BIRKHOFF FOR COMPACT DISSIPATIVE DYNAMICAL SYSTEMS(Academy of Sciences of Moldova, 2015) Ceban, DavidIn this paper we prove the analogues of Birkhoff’s theorem foronesided dynamical systems (both with continuous and discretetimes) with noncompactspace having a compact global attractor. The relation between Levinson center, chainrecurrent set and center of Birkhoff is established for compact dissipative dynamicalsystems.