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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.
GLOBAL ATTRACTORS OF NON-AUTONOMOUS DIFFERENCE EQUATIONS
(Institutul de Matematică şi Informatică al AŞM, 2009) Cheban, David; Mammana, Cristina; Michetti, Elizabetta
The article is devoted to the study of global attractors of quasi-linear non-autonomous di®erence equations. The results obtained are applied to the study of a triangular economic growth model T : R2 ! R2 recently developed in S. Brianzoni, C. Mammana and E. Michetti [1