The structure of global attractors for non-autonomous perturbations of discrete gradient-like dynamical systems

Cheban David; Mammana Cristiana; Michetti Elisabetta

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2018-07-10 17:41

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CHEBAN, David, MAMMANA, Cristiana, MICHETTI, Elisabetta. The structure of global attractors for non-autonomous perturbations of discrete gradient-like dynamical systems. In: Journal of Difference Equations and Applications, 2016, nr. 11(22), pp. 1673-1697. ISSN 0022-6198. DOI: https://doi.org/10.1080/10236198.2016.1234616

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Journal of Difference Equations and Applications

Numărul 11(22) / 2016 / ISSN 0022-6198 /ISSNe 1090-2732

The structure of global attractors for non-autonomous perturbations of discrete gradient-like dynamical systems

DOI:https://doi.org/10.1080/10236198.2016.1234616

Pag. 1673-1697

Cheban David¹, Mammana Cristiana², Michetti Elisabetta²

¹ Moldova State University,
² Università degli Studi di Macerata

Disponibil în IBN: 8 noiembrie 2017

Rezumat

In this paper we give the complete description of the structure of compact global (forward) attractors for non-autonomous perturbations of discrete autonomous gradient-like dynamical systems under the assumption that the original discrete autonomous system has a finite number of hyperbolic stationary solutions. We prove that the perturbed non-autonomous (in particular τ-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff) system has exactly the same number of invariant sections (in particular the perturbed systems has the same number of τ-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff solutions). It is shown that the compact global (forward) attractor of non-autonomous perturbed system coincides with the union of unstable manifolds of this finite number of invariant sections.

Cuvinte-cheie
almost periodic and almost automorphic solutions,

chain-recurrent motions, global attractor, Gradient-like dynamical systems, non-autonomous perturbations

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