Paradigms of the Large-Scale Universe  book cover
1st Edition

Paradigms of the Large-Scale Universe



ISBN 9782881249662
Published November 4, 1994 by CRC Press
160 Pages

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Book Description

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

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

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Author(s)

Biography

Grigor A. Gurzadyan (Author)