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

Autor(es)

Bortolan, M. C. ^[1] ; Carvalho, A. N. ^[2] ; Langa, J. A. ^[3] ; Raugel, G. ^[4]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Dynamics and Differential Equations; OCT 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 10/52329-8 - Qualitative aspects of infinite dimensional dynamical systems. (FAPESP-CNRS)
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/10997-6 - Robusteza de atratores sob perturbações autônomas ou não-autônomas: Estabilidade estrutural
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 12/23724-1 - Dinâmica assintótica de processos de evolução
• Beneficiário: Matheus Cheque Bortolan
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 10/50690-5 - Estimativas da dimensao fractal para atratores globais em semigrupos gradient-like generalizados
• Beneficiário: Matheus Cheque Bortolan
• Modalidade de apoio: Bolsas no Brasil - Doutorado