Time evolution of non linear dynamical systems often generate complex (irregular) time series. The assumption that a time series come from a dynamical system leads to a variety of concepts and tools enriching the statistical methods of analysis.
The two main approaches are topological and statistical, we will mostly concentrate on the second one.
We will emphasize the relations between the theoretical concepts and the algorithms developed to measure/quantify the complexity of dynamical systems.
Various topics will be discussed: ergodicity, Lyapunov exponents,reconstruction of attractors, dimension, entropy, noise reduction, prediction.
These concepts and the associated tools can be used in broader contexts where the underlying generating dynamical system is not clearly identified.
