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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2021.tde-17032021-121711
Document
Author
Full name
Carlos Roberto Takaessu Junior
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2021
Supervisor
Committee
Carvalho, Alexandre Nolasco de (President)
Bonotto, Everaldo de Mello
Madeira, Gustavo Ferron
Silva, Marcio Antonio Jorge da
Title in English
Gradient structure of the cascade system
Keywords in English
Cascade system
Dynamical systems
Semigroups
Abstract in English
In this work we approach the theory necessary to solve one of the problems present in the article (ARAGÃO-COSTA et al., 2013), related to the cascade system. The present paper is divided in three parts: the first part is dedicated to study results and concepts from autonomous dynamical systems, such as the robustness of gradient semigroups, for example. The second part is dedicated to the concepts of non-autonomous dynamical systems like pullback attractors, exponential dichotomy and hyperbolic global solutions. The third part is the application, related to the cascade systems, of the first two chapters. Even though the cascade systems are autonomous, it benefits considerably from the theory of non-autonomous attractors, in particular of the skew-product formulation.
Title in Portuguese
Estrutura gradiente de sistemas do tipo cascata
Keywords in Portuguese
Semigrupos
Sistema cascata
Sistemas dinâmicos
Abstract in Portuguese
Neste trabalho abordamos a teoria necessária para resolver um dos problemas presentes no artigo (ARAGÃO-COSTA et al., 2013), relacionado ao sistema do tipo cascata. O presente trabalho está dividido em três partes: a primeira parte dedica-se a estudar resultados e conceitos de sistemas dinâmicos autônomos, como a robusteza de semigrupos gradiente, por exemplo. A segunda parte dedica-se a conceitos da teoria de sistemas dinâmicos não autônomos como atratores pullback, dicotomia exponencial e soluções globais hiperbólicas. A terceira parte é a aplicação, relacionada aos sistemas do tipo cascata, das duas primeiras partes. Apesar dos sistemas do tipo cascata serem autônomos, tais sistemas se beneficiam da teoria de atratores não autônomos, em particular dos conceitos de skew-product.
 
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Publishing Date
2021-03-17
 
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