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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

NON-AUTONOMOUS MORSE-DECOMPOSITION AND LYAPUNOV FUNCTIONS FOR GRADIENT-LIKE PROCESSES

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Author(s):
Aragao-Costa, E. R. [1] ; Caraballo, T. [2] ; Carvalho, A. N. [1] ; Langa, J. A. [2]
Total Authors: 4
Affiliation:
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, E-41080 Seville - Spain
Total Affiliations: 2
Document type: Journal article
Source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 365, n. 10, p. 5277-5312, OCT 2013.
Web of Science Citations: 9
Abstract

We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) and prove that a non-autonomous gradient-like evolution process possesses a Morse-decomposition on the associated pullback attractor. We also prove the existence of an associated Lyapunov function which describes the gradient behavior of the system. Finally, we apply these abstract results to non-autonomous perturbations of autonomous gradient-like evolution processes (semigroups or autonomous dynamical systems). (AU)