2. Articole

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Author: search.filters.author.Cheban, DavidSubject: 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.