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.
Preface
Acknowledgements
Glossary
The Problem of the Large-Scale Structure of the Universe
Outlook of Main Issues
The Observations: A Bird’s Eye View
Geometry, Dynamical Systems, Catastrophes
Geometry
Dynamical Systems
Catastrophes
Galaxy Clusters
The Cluster as a Basic Concept
Clusters Defined by Dynamical Systems
S-Tree
The S-Tree Technique
The Measure of Influence
Computer Analysis Strategy
Substructure of Real Filaments: I. Local Group; II. Abell 754
Appearance of the Matter Distribution
Fractals
Hausdorff Dimension and Physical Characteristics of the Filaments
Sheet-Like Structures as Elementary Catastrophes
Statistical Methods
Correlation Functions
Topological Measures
Minimal Spanning Tree
Wavelet Transform
Filaments and Light-Travel Effects
Dynamical Equations of Cosmology
Light-Cone Effects
Cosmological Parameters
The Cosmic Background Radiation as a Tracer of Geometry of the Universe
The Crucial Feature of the Background Radiation
Free Motion in the World
Photon Beam Mixing in the Closed Friedmann Universe
Degree of Complexity of Anisotropy Spots
Photons, Billiards, Ink Drops, Etc.
Epilogue
Index
Biography
Grigor A. Gurzadyan (Author)
