2. Articole

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Subject: search.filters.subject.global attractor

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    INVARIANT MANIFOLDS, GLOBAL ATTRACTORS AND ALMOST PERIODIC SOLUTIONS OF NONAUTONOMOUS DIFFERENCE EQUATIONS
    (Elsevier, 2004) Cheban, David; Mammana, Cristiana
    The article is devoted to the study of quasi-linear nonautonomous difference equations: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets. First, we prove that such equations admit an invariant continuous section (an invariant manifold). Then, we obtain the conditions for the existence of a compact global attractor and characterize its structure. Third, we derive a criterion for the existence of almost periodic and recurrent solutions of the quasi-linear nonautonomous difference equations. Finally, we prove that quasi-linear maps with chaotic base admit a chaotic compact invariant set. The obtained results are applied while studying triangular maps: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets.
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    ALMOST PERIODIC SOLUTIONS AND GLOBAL ATTRACTORS OF NON-AUTONOMOUS NAVIER–STOKES EQUATIONS
    (Springer, 2004) Cheban, David; Duan, Jinqiao
    The article is devoted to the study of non-autonomous Navier–Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier–Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic, almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier–Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier–Stokes equations.
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    BIRKHOFF'S CENTER OF COMPACT DISSIPATIVE DYNAMICAL SYSTEMS
    (Valines SRL, 2014) Cheban, David
    We introduce the notion of Birkhoff center for arbitrary dynamical systems admitting a compact global attractor. It is shown that Birkhoff center of dynamical system coincides with the closure of the set of all positively Poisson stable points of dynamical system.
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    ASYMPTOTIC STABILITY OF INFINITE-DIMENSIONAL NONAUTONOMOUS DYNAMICAL SYSTEMS
    (Academy of Sciences of Moldova, 2013) Ceban, David
    This 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 Equations