This unique book offers a new approach to the study of the large-scale structure of the Universe. Though considered to be governed by the same Newtonian gravitational interaction, the dynamics of galactic clusters differs drastically from that of stellar dynamics, and therefore a different mathematical approach is required. The theory of dynamical systems provides a powerful method for the study of the profound properties of multi-dimensional nonlinear systems.

This monograph offers a consistent geometrical treatment of observational cosmology from the concepts of the theory of dynamical systems.

Since this mathematical technique is not yet a familiar tool in the field of astrophysics, a summary of the fundamental ideas of differential geometry, ergodic theory and catastrophe theory is presented. Such a unified approach facilitates the study of a wide range of, at first sight, very different phenomena within the same physical framework, thus revealing their universal underlying properties.

This book will be of great value to astrophysicists and mathematicians for its pioneering approach to the study of the large-scale Universe.