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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.)

Nonautonomous Perturbations of Morse-Smale Semigroups: Stability of the Phase Diagram

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Author(s):
Bortolan, M. C. [1] ; Carvalho, A. N. [2] ; Langa, J. A. [3] ; Raugel, G. [4]
Total Authors: 4
Affiliation:
[1] Univ Fed Santa Catarina, Florianopolis, SC - Brazil
[2] Univ Sao Paulo, Sao Carlos, SP - Brazil
[3] Univ Seville, Seville - Spain
[4] Univ Paris Sud, CNRS, Orsay - France
Total Affiliations: 4
Document type: Journal article
Source: Journal of Dynamics and Differential Equations; OCT 2021.
Web of Science Citations: 0
Abstract

In this work we study Morse-Smale semigroups under nonautonomous perturbations, which leads us to introduce the concept of Morse-Smale evolution processes of hyperbolic type, associated to nonautonomous evolutionary equations. They are amongst the dynamically gradient evolution processes (in the sense of Carvalho et al., in: Applied Mathematical Sciences, vol 182, Springer, New York, 2013) with a finite number of hyperbolic global solutions, for which the stable and unstable manifolds intersect transversally. We prove the stability of the phase diagram of the attractors for a small continuously differentiable nonautonomous perturbation [T-eta(t, s) : (t, s) is an element of P] of a Morse-Smale semigroup [T (t) : t >= 0] with a finite number of hyperbolic equilibria. We present the complete proofs of the local and global lambda-lemmas in the infinite-dimensional case. Such results are due to D. Henry, presented in his handwritten notes Henry (in: Manuscript, IME-USP), and are included here for completeness. (AU)

FAPESP's process: 10/52329-8 - Qualitative aspects of infinite dimensional dynamical systems
Grantee:Alexandre Nolasco de Carvalho
Support Opportunities: Regular Research Grants
FAPESP's process: 18/10997-6 - Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability
Grantee:Alexandre Nolasco de Carvalho
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 12/23724-1 - Asymptotical dynamics of evolution processes
Grantee:Matheus Cheque Bortolan
Support Opportunities: Scholarships in Brazil - Post-Doctoral