Estructura topológica de flujos caóticos

Institución otorgante:

Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales

Fecha:

2001

Tipo de documento: 

info:eu-repo/semantics/doctoralThesis
 

Formato:

application/pdf

Idioma:

spa

Temas:

ANALISIS DE SERIES TEMPORALES - CAOS - TEMPLADOS - GRUPOS DE HOMOLOGIA - TEMPORAL SERIES ANALYSIS - CHAOS - TEMPLATES - HOMOLOGY GROUPS

Descripción:

The analysis of data has been enriched with the tools of non linear dynamics. For the case of deterministic systems with chaotic behaviour, the topologicaldescription of reconstructed flows has been very successful. However,the state of the subject at the beginning of this had the restriction of dimensionality (three) for the underlying phase spaces. This thesis presents atopological technique for data analysis based on the description of branchedmanifolds that hold the underlying dynamics. The description is carriedout through a series of invariants of algebraic topology known as homologygroups. The method extends the applicability of the topological approachto the analysis of data, for short and noisy temporal series and for seriesembedded in a number of dimensions higher than three. Apart from theintroduction to this perspective, we present algorythms, numerical examplesand experimetnal examples of this technique.

Identificador:

https://hdl.handle.net/20.500.12110/tesis_n3356_Sciamarella