Book:P.G. Drazin/Nonlinear Systems
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P.G. Drazin: Nonlinear Systems
Published $\text {1992}$, 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
Source work progress
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