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Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems
Drawing on the middle chapters from the first edition of J. Barkley Rosser's seminal work, From Catastrophe to Chaos, this book presents an unusual perspective on economics and economic analysis. Current economic theory largely depends upon assuming that the world is fundamentally continuous. However, an increasing amount of economic research has been done using approaches that allow for discontinuities such as catastrophe theory, chaos theory, synergetics, and fractal geometry. The spread of such approaches across a variety of disciplines of thought has constituted a virtual intellectual revolution in recent years. This book reviews the applications of these approaches in various subdisciplines of economics and draws upon past economic thinkers to develop an integrated view of economics as a whole from the perspective of inherent discontinuity.
Introducing Chaos
If a butterfly flaps its wings in Brazil, does it cause a tornado in Texas? Chaos theory attempts to answer such baffling questions. The discovery of randomness in apparently predictable physical systems has evolved into a science that declares the universe to be far more unpredictable than we have ever imagined. Introducing Chaos explains how chaos makes its presence felt in events from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern maths and physics, and explores the relationship between chaos and complexity, the unifying theory which suggests that all complex systems evolve from a few simple rules. This is an accessible introduction to an astonishing and controversial theory.
Wavelets Through a Looking Glass
? Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource.; New previously unpublished results appear on the homotopy of multiresolutions, approximation theory, the spectrum and structure of the fixed points of the associated transfer, subdivision operators; Key topics of wavelet theory are examined; Excellent graphics show how wavelets depend on the spectra of the transfer operators; The important role of the spectrum of a transfer operator is studied; This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory.
The Mathematician's Brain
The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries. Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code durin...
Living Record Of Scientific History, The: Conversations With C N Yang
Professor Chen-Ning Yang is best known for his achievements in Physics. He has also made significant contributions to the development of mathematics, as mathematics is extensively used in his research. In his long and fruitful academic career, he has witnessed many important events in the fields of Physics and Mathematics, and has collaborated or interacted with many great scientists in history. This book records eight interviews with Professor Chen-Ning Yang, which were conducted by the authors from 2016 to 2019.Through Professor Yang's unique perspective, major scientific events in the 20th century were revisited vividly, elaborating the development and mutual influences of mathematics and physics, as well as unveiling the academic work, the daily lives, and the personalities of scientists, as well as their collaboration and competition, some stories unknown to the public before are also revealed in this book.
Chance and Chaos
How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic.
Statistical Mechanics: Rigorous Results
This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.
Mosaic
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Turbulence, Strange Attractors And Chaos
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.
