2. Articole

Permanent URI for this collectionhttps://msuir.usm.md/handle/123456789/17

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Author: search.filters.author.Cheban, DavidSubject: search.filters.subject.skew-product flow

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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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    GLOBAL ATTRACTORS FOR V -MONOTONE NONAUTONOMOUS DYNAMICAL SYSTEMS
    (Institutul de Matematică şi Informatică al AŞM, 2003) Cheban, David; Kloeden, Peter-E.; Schmalfuss, Bjorn
    This article is devoted to the study of the compact global atrractors of Vmomotone nonautonomous dynamical systems.We give a description of the structure of compact global attractors of this class of systems. Several applications of general results for different classes of differential equations (ODEs, ODEs with impulse, some classes of evolutionary partial differential equations) are given.