{'fraction_non_alphanumeric': 0.017321785476349102, 'fraction_numerical': 0.002331778814123917, 'mean_word_length': 5.103658536585366, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dynamical Systems in Cosmology

The aim of this book is to show the effectiveness of the theory of dynamical systems in cosmological applications. It is the result of a workshop held at Cape Town, 27 June - 2 July 1994; however, it is much more than the usual conference proceedings, it is not just a collection of articles but rather a collectively written monograph. The fact that the book only deals with finite-dimensional dynamical systems limits the applications of this theory to the study of dynamics governed by Einstein's equations, which can be reduced to the form of ordinary differential equations. This class contains homogeneous Bianchi solutions and some non-homogeneous cosmological models with group. Additionally, the evolution of density perturbations in the Universe and the dynamics of so-called silent universes are also discussed. Some other standard applications of the theory of dynamical systems, for instance, integrability problems, are absent from the book. The essence of the theory of dynamical systems is not the study of particular solutions as represented by trajectories in the phase space, but rather the study of all possible solutions for all admissible initial conditions. The initial conditions are usually given by measurements, and hence they are known with a finite precision. Consequently, in phase space they do not distinguish single trajectories, but rather a class of trajectories given by nearby initial conditions. The exceptional character of the book is guaranteed by the fact that its authors combine theoretical dynamical investigations with observational data. This circumstance distinguishes the present book from the one written by O I Bogoyavlensky, which also contains a few chapters devoted to the analysis of multi-dimensional dynamical systems with application to Bianchi cosmology. In my opinion, both books are complementary, and together beautifully present the actual state of the art in the field of applications of the theory of dynamical systems to general relativity and cosmology. In the class of Bianchi models regular and chaotic behaviours coexist. Chaotic dynamics is studied by D Hobill who gives a simple estimate showing that the age of the Universe is too short for chaotic effects to have developed. This suggests that from the point of view of homogeneous cosmology, chaotic solutions have only a limited significance. Will this conclusion be valid in a general case? It seems that in non-homogeneous cosmology, chaotic dynamics is important, but it must be described by infinite-dimensional dynamical systems. Of course, the research in this field should start from simpler cases not necessarily confirmed by observations. In this sense, the present book is highly relevant. It does not often happen that scientific meetings and conferences give such concrete results as those presented in this monograph. I admire the determination and the quality of the editors' and authors' work which results in so valuable a book.