Characterisation of time series from non-linear systems

The extraction of fractal dimensions and Lyapunov exponents of experimental time series has become an important instrument in analysing the dynamic properties of nonlinear dynamical systems. The accuracy of these calculations as well as the success of noise reduction processes and forecasting methods depends strongly on the quality of the phase space reconstructed with delay time coordinates. Therefore, methods are presented which yield optimal embedding parameters. To ensure the correct calculation of fractal dimensions and Lyapunov exponents the noise level on experimental data has to be reduced. A robust noise reduction algorithm working in phase space is discussed