Estructura topológica de flujos caóticos - Sciamarella, Denisse (2001)
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.