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Robustness of the dynamics under perturbations: from the upper semicontinuity to the structural stability

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Author(s):
Arthur Geromel Fischer
Total Authors: 1
Document type: Master's Dissertation
Press: São Carlos.
Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
Defense date:
Examining board members:
Hildebrando Munhoz Rodrigues; Alexandre Nolasco de Carvalho; Sergio Muniz Oliva Filho; Gerson Petronilho
Advisor: Hildebrando Munhoz Rodrigues
Abstract

The main goal of this work is the study of structural stability of global attractors. We start this work by presenting the concept and basic properties of semigroups and global attractors. We then studied gradient and dinamically gradient semigroups, showing that these concepts are equivalent and that a small autonomous pertubation of a gradient semigroup remains a gradient semigroup. We studied the stable and unstable manifolds in the neighbourhood of a hyperbolic equilibrium point and the behavior of periodic solutions under perturbation. Finally, we studied the Morse-Smale semigroups. (AU)