Teoria da matriz de transição

Author(s)

Ewerton Rocha Vieira

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2015-05-03

Examining board members

Ketty Abaroa de Rezende; Maria do Carmo Carbinatto; Oziride Manzoli Neto; Mariana Rodrigues da Silveira; Marcio Fuzeto Gameiro

• Advisor: Ketty Abaroa de Rezende

Abstract

In this thesis, we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well as the verification that each of the previous transition matrices are cases of the (generalized) transition matrix. Furthermore, we address how applications of the previous transition matrices to the Conley Index theory carry over to the (generalized) transition matrix. When this more general transition matrix satisfies the additional requirement that it covers flow-defined Conley-index isomorphisms, one proves algebraic and connection-existence properties. These general transition matrices with this covering property are referred to as generalized topological transition matrices and are used to consider connecting orbits of Morse-Smale flows without periodic orbits, as well as those in a continuation associated to a dynamical spectral sequence (AU)

• FAPESP's process: 10/19230-8 - Transition Matrix Theory
• Grantee: Ewerton Rocha Vieira
• Support Opportunities: Scholarships in Brazil - Doctorate