Chaotic Phenomena in Astrophysics and Cosmology

Chaos is a typical property of many‐dimensional nonlinear systems and is revealed in a number of problems of astrophysics and cosmology. Particularly, chaos made to revise the two‐hundred year old views on the evolution of Solar system, while the theory of interstellar matter, dynamics of stellar systems cannot be considered neglecting the chaotic effects. The lectures notes cover the following topics: dynamics of the Solar system, relaxation of galaxies and star clusters, the substructure of galaxy clusters, hyperbolicity in the Wheeler‐DeWitt superspace and the stability of cosmological solutions. Thus we aimed to cover as broad topics as possible, at the same time showing the diversity of approaches and mathematical tools. For pedagogical reasons, the techniques such as the estimation Kolmogorov‐Sinai entropy, the hyperbolicity in pseudo‐Riemannian spaces are described in some detail, so that they can be applied in various problems.