Many applications of science and engineering, e.g. in physics, biology, economics or meteorology, are determined by dynamical systems. These systems evolve over time and then generate a set of data spaced in time, called time series. The analysis of time series from real systems, in terms of nonlinear dynamics, is the most direct link between chaos theory and the real world. Very useful information for making predictions about dynamical systems is extracted from the analysis of these time series. Since many of these applications must provide a real time response, it is necessary for analysis and prediction to be performed on a reasonable time scale. High Performance Computing gives a feasible solution to this problem, which enables it to be solved in an efficient manner. Nowadays, parallel computing is one of the most appropriate ways of obtaining important computational power. Thus, a set of high performance algorithms has been developed in this Thesis for both nonlinear time...

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