Book:P.G. Drazin/Nonlinear Systems

Subject Matter

 * Non-Linear Systems

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