This text offers a geometrical treatment of observational cosmology from the concepts of the theory of dynamical systems. Since mathematical techniques are not a familiar tool in this field, a summary of the ideas of differential geometry, ergodic theory and catastrophe theory is included.

Dynamical systems provide powerful methods for the study of profound properties of many-dimensional nonlinear systems. In this unique book, the authors offer a consistent geometrical treatment of observational cosmology from the concepts of the theory of dynamical systems. The dynamics of clusters of galaxies differ drastically from stellar dynamics, thus requiring a mathematical approach to large-scale problems. Since mathematical techniques are not a familiar tool in this field, a full summary of the elementary ideas of differential geometry, ergodic theory and catastrophe theory are also considered in this exploratory text. Readership: Mathematicians, astrophysicists, and cosmologists, as well as anyone interested in the many subject disciplines related to geometrical and topological aspects of the large-scale universe.

The problem of large-scale structure of the universe
geometry, dynamical systems, catastrophes
definition of a galaxy cluster
the bound-tree technique
appearance of matter distribution
statistical methods
filaments and light-travel effects
the cosmic background radiation as a tracer of geometry of the universe.