# Book:P.G. Drazin/Nonlinear Systems

## 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*