The authors explore the origin of multidimensional strange attractors and their role in describing turbulence. It includes an analytical estimation of the deminsions of strange attractors for models described by differential-difference equations and discusses the conditions in which space-homogeneous chaos is stable with respect to random perturbations in flow systems.

The present collection of reprints covers the main contributions of David Ruelle, and coauthors, to the theory of chaos and its applications. Several of the papers reproduced here are classics in the field. Others (that were published in less accessible places) may still surprise the reader.The collection contains mathematical articles relevant to chaos, specific articles on the theory, and articles on applications to hydrodynamical turbulence, chemical oscillations, etc.A sound judgement of the value of techniques and applications is crucial in the interdisciplinary field of chaos. For a critical assessment of what has been achieved in this area, the present volume is an invaluable contribution.

Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.

This authoritative handbook explores the latest integrated theory for understanding human language, offering the most inclusive text yet published on the rapidly evolving emergentist paradigm. Brings together an international team of contributors, including the most prominent advocates of linguistic emergentism Focuses on the ways in which the learning, processing, and structure of language emerge from a competing set of cognitive, communicative, and biological constraints Examines forces on widely divergent timescales, from instantaneous neurolinguistic processing to historical changes and language evolution Addresses key theoretical, empirical, and methodological issues, making this handbook the most rigorous examination of emergentist linguistic theory ever

The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.

Four years have elapsed since the preparation of the original Russian version of this book. This is a long time when dealing with such actively expanding fields of oceanography as research into small-scale structures and the investigation of hydro physical processes. Over this period new quick-response devices have been developed and successfully used for measurements taken in various ocean areas. Improvements in high-frequency meters used to measure hydrophysical parameters has enabled workers to obtain more accurate absolute values of the fluctuations measured by such devices. In view of this scientific progress, some of the ideas presented in this book now require additional explanation. Great care should be used in dealing with the absolute fluctuation values of hydro physical fields, since the methods used for the determination of the accuracy of the high-frequency measuring devices have been imperfect in the past. Never theless, it would appear that the results of the investigations summarized in this book have not lost their importance, and that the established laws governing small-scale pro cesses in the ocean are of a sufficiently universal nature and, as such, have not been shattered with the qualitative and quantitative advances in devices used for measurements taken in oceans. The authors feel that their work is of interest to English-speaking readers. The appearance of the English translation of the book is, to a very large extent, due to the tremendous amount of editing work brilliantly done by Prof. H. Tennekes.

The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.