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.
Table of Contents
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.
Grigor A. Gurzadyan (Author)