Time series analysis and correlation dimension estimation: Mathematical foundation and applications

A time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The embedding theorems and their relationship with dimension preservation are reviewed in detail, but more attention is focussed on the concept development.