The structure of global attractors for non-autonomous perturbations of discrete gradient-like dynamical systems. Issue 11 (1st November 2016)

• Record Type: Journal Article
• Authors: Cheban, D.; Mammana, C.; Michetti, E.
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 11(2016)
• Page Start: 1673
• Page End: 1697
• Publication Date: 2016-11-01
• Subjects: Global attractor -- gradient-like dynamical systems -- non-autonomous perturbations -- chain-recurrent motions -- almost periodic and almost automorphic solutions; Primary: 37B35 -- 37B55 -- 34C27 -- 35B15 -- 35B20 -- 35B41; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2016.1234616
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : 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 particularτ -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 ofτ -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.