O indice homotopico de Conley para aplicações continuas
AUTOR(ES)
Rogerio Casagrande
DATA DE PUBLICAÇÃO
2002
RESUMO
The topic we develop in this monograph pertains to the general area of discrete dynamical systems and our goal is to study the discrete Conley index, a homotopic invariant of the dynamics. This index has been developed mainly within the past 15 years, inspired on the continuous case. Qur approach is to develop the index as in Franks and Richeson [FrRi]. We introduce the concepts of maximal invariant sets, isolated invariant sets S of a continuous function, filtration pairs for S, among others. In order to define the index we use the relation of shift equivalence, an important equivalence relation. We show that the shift equivalence class of the pointed space map is an invariant of the choice of a filtration pair. We present some examples for real valued functions, including ones with chaotic behaviour as the one-dimensional horseshoe. We present a short summary of prior developments of the index using category theory due to 8zymczak [8z] and a cohomological version due to Mrozek [Mr] in order to contrast with the theory of the discrete Conley index presented by Franks and Richeson. We show that the definitions of the index due to Franks-Richeson and Szymczak are equivalent
ASSUNTO(S)
topologia algebrica caos quantico sistemas dinamicos diferenciais
