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Introduction To Nonlinear Dynamics For Physicists : World Scientific Lecture Notes In Physics - H.D.I. Abarbanel

Introduction To Nonlinear Dynamics For Physicists

World Scientific Lecture Notes In Physics

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This is a series of lecture notes on nonlinear dynamics for physicists. The level is that of an advanced undergraduate or beginning graduate student. The main aim of these lectures is to present a balance of qualitative and quantitative material. The book also aims to address three main questions about nonlinear dynamics: what is nonlinear dynamics all about and what makes it differ from linear dynamics which permeate all familiar textbooks?; from the physicist's point of view, why should we study nonlinear systems and leave the comfortable territory of linearity?; and how can one progress in the study of nonlinear systems both in the analysis of these systems when we know them, and in learning about new systems from observations of their experimental behaviour? As it would be impossible to answer these questions in the finest detail, this volume nevertheless points the way for the interested reader. Useful problems have also been incorporated as a guide.

Introductionp. 1
Nonlinear Oscillator without Dissipationp. 6
Equilibrium States of a Nonlinear Oscillator with Dissipationp. 11
Oscillations Systems with Nonlinear Dissipation-Generatorsp. 17
The Van der Pol Generatorp. 22
The Poincare Mapp. 27
Slow and Fast Motions in Systems with One Degree of Freedomp. 33
Forced Nonlinear Oscillators: Linear and Nonlinear Resonancesp. 38
Forced Generator: Synchronizationp. 45
Competition of Modesp. 51
Poincare Indices and Bifurcations of Equilibrium Statesp. 55
Resonance Interactions between Oscillatorsp. 62
Solitonsp. 69
Steady Propagation of Shock Wavesp. 80
Formation of Shock Wavesp. 86
Solitons. Shock Waves. Wave Interaction. The Spectral Approachp. 89
Weak Turbulence. Random Phase Approximationp. 95
Regular Patterns in Dissipative Mediap. 100
Deterministic Chaos. Qualitative Descriptionp. 104
Description of a Circuit with Chaos. Chaos in Mapsp. 111
Bifurcations of Periodic Motions. Period Doublingp. 116
Controlled Nonlinear Oscillator. Intermittencyp. 122
Scenarios of the Onset of Chaos. Chaos through Quasi-Periodicityp. 132
Characteristics of Chaos. Experimental Observation of Chaosp. 139
Multidimensional Chaos. Discrete Ginzburg-Landau Modelp. 147
Problems to Accompany the Lecturesp. 151
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810214104
ISBN-10: 9810214103
Series: World Scientific Lecture Notes In Physics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 168
Published: 1st June 1993
Country of Publication: SG
Dimensions (cm): 21.59 x 15.24  x 1.27
Weight (kg): 0.24

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