1st Edition

Paradigms of the Large-Scale Universe

By Grigor A. Gurzadyan Copyright 1994
    160 Pages
    by CRC Press

    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 the Large-Scale Structure of the Universe

    Outlook of Main Issues

    The Observations: A Bird’s Eye View

    Geometry, Dynamical Systems, Catastrophes


    Dynamical Systems


    Galaxy Clusters

    The Cluster as a Basic Concept

    Clusters Defined by Dynamical Systems


    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


    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.




    Grigor A. Gurzadyan (Author)