Book:P.G. Drazin/Nonlinear Systems

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P.G. Drazin: Nonlinear Systems

Published $1992$, Cambridge University Press

ISBN 0-521-40668-4.


Subject Matter


Contents

Preface
1 Introduction
1 Nonlinear systems, bifurcations and symmetry breaking
2 The origin of bifurcation theory
3 A turning point
4 A transcritical bifurcation
5 A pitchfork bifurcation
6 A Hopf bifurcation
7 Nonlinear oscillations of a conservative system
8 Difference equations
9 An experiment on statics
Further reading
Problems
2 Classification of bifurcations of equilibrium points
1 Introduction
2 Classification of bifurcations in one dimension
3 Imperfections
4 Classification of bifurcations in higher dimensions
Further reading
Problems
3 Difference equations
1 The stability of fixed points
2 Periodic solutions and their stability
3 Attractors and volume
3.l Attractors
3.2 Volume
4 The logistic equation
5 Numerical and computational methods
6 Some two-dimensional difference equations
7 Iterated maps of the complex plane
Further reading
Problems
*4 Some special topics
1 Cantor sets
2 Dimension and fractals
3 Renormalization group theory
3.1 Introduction
3.2 Feigenbaum's theory of scaling
4 Liapounov exponents
Further reading
Problems
5 Ordinary differential equations
1 Introduction
2 Hamiltonian systems
3 The geometry of orbits
*4 The stability of a periodic solution
Further reading
Problems
6 Second-order autonomous differential systems
1 Introduction
2 Linear systems
3 The direct method of Liapounov
4 The Lindstedt-Poincaré method
5 Limit cycles
6 Van der Pol's equation
Further reading
Problems
7 Forced oscillations
1 Introduction
2 Weakly nonlinear oscillations not near resonance: regular perturbation theory
3 Weakly nonlinear oscillations near resonance
4 Subharmonics
Further reading
Problems
8 Chaos
1 The Lorenz system
2 Duffing's equation with negative stiffness
*3 The chaotic break-up of a homoclinic orbit: Mel'nikov's method
4 Routes to chaos
5 Analysis of time series
Further reading
Problems
*Appendix: Some partial-differential problems
Answers and hints to selected problems
Bibliography and author index
Motion picture and video index
Subject index