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This festschrift is dedicated to Professor Howell Tong on the occasion of his 65th birthday. With a Foreword written by Professor Peter Whittle, FRS, it celebrates Tong's path-breaking and tireless contributions to nonlinear time series analysis, chaos and statistics, by reprinting 10 selected papers by him and his collaborators, which are interleaved with 17 original reviews, written by 19 international experts. Through these papers and reviews, readers will have an opportunity to share many of the excitements, retrospectively and prospectively, of the relatively new subject of nonlinear time series. Tong has played a leading role in laying the foundation of the subject; his innovative and authoritative contributions are reflected in the review articles in the volume, which describe modern and related developments in the subject, including applications in many major fields such as ecology, economics, finance and others. This volume will be useful to researchers and students interested in the theory and practice of nonlinear time series analysis. Sample Chapter(s). Foreword (68 KB). Chapter 1: Birth of the Threshold Time Series Model (269 KB). Contents: Reflections on Threshold Autoregression (P J Brockwell); The Threshold Approach in Volatility Modelling (W K Li); Dependence and Nonlinearity (M Rosenblatt); Recent Developments on Semiparametric Regression Model Selection (J Gao); Thoughts on the Connections Between Threshold Time Series Models and Dynamical Systems (D B H Cline); Crossing the Bridge Backwards: Some Comments on Early Interdisciplinary Efforts (C D Cutler); On Likelihood Ratio Tests for Threshold Autoregression (K-S Chan & H Tong); An Adaptive Estimation Method for Semiparametric Models and Dimension Reduction (C Leng et al.); On Howell Tong's Contributions to Reliability (M M Ali); and other papers. Readership: Graduate students and researchers in statistics and related fields of ecology, economics and finance.
Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations. No prior knowledge of Maple is assumed. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.
The most important characteristic of the “world filled with nonlinearity” is the existence of scale interference: disparate space–time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly. This leads to various peculiar phenomena such as chaos, critical phenomena, and complex biological phenomena, among others. Conceptual analysis and phenomenology are the keys to describe and understand phenomena that are subject to scale interference, because precise description of unfamiliar phenomena requires precise concepts and their phenomenological description. The book starts with an illustration of conceptual analysis in terms of chaos and randomness, and goes on to explain renormalization group philosophy as an approach to phenomenology. Then, abduction is outlined as a way to express what we have understood about the world. The book concludes with discussions on how we can approach genuinely complex phenomena, including biological phenomena. The main target of this volume is young people who have just started to appreciate the world seriously. The author also wishes the book to be helpful to those who have been observing the world, but who wish to appreciate it afresh from a different angle.
Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations. No prior knowledge of Maple is assumed. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.
The author argues that we have reached the nadir of the adaptive range of our industrialised world. Now faced with an unsustainable trilemma of social, organisational and economic complexity, we have entered an era in which the rules we have previously organised our lives around no longer apply. Leaving us with both a design problem and a design challenge which we must urgently solve. By describing an entirely new way for true social, economic and organisational innovation to happen, No straight lines presents a revolutionary logic and an inspiring plea for a more human-centric world.
"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.
Nonlinear concepts from chaos theory, complexity studies, and fractal geometry have transformed the way we think about the mind. Nonlinear Psychoanalysis shows how nonlinear dynamics can be integrated with psychoanalytic thinking to shed new light on psychological development, therapeutic processes, and fundamental psychoanalytic concepts. Starting with a personal history of the author’s engagement with nonlinear dynamics and psychoanalysis, this book describes how his approach applies to diagnosis of psychological conditions, concepts of normal and pathological development, gender, research methods, and finally the theory and practice of psychoanalysis and psychodynamic psychotherapy. This book is full of new ideas about the basic nonlinear processes of human development, nonlinear views of gender and fundamental psychoanalytic process like working through, and the nature of the therapeutic process as conceptualized in terms of the theory of coupled oscillators. Galatzer-Levy questions many standard psychoanalytic formulations and points to a freer practice of psychoanalysis and psychoanalytic thinking. His new approach opens the reader’s eyes to ways in which development and treatment can occur through processes not now included in standard psychoanalytic theory. The book not only provides useful theories but also helps readers take note of commonly passed over phenomena that were unseen for lack of a theory to explain them. Galatzer-Levy brings an unusual combination of training in psychiatry, psychoanalysis, and mathematics to this unique study, which summarizes his forty years of exploration of nonlinearity and psychoanalysis. Nonlinear Psychoanalysis will appeal to psychoanalysts and psychotherapists as well as students of nonlinear dynamics systems.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.