Front Matter....Pages i-xx Linear Oscillators....Pages 1-22 Oscillations in a System with Two Linked Oscillators....Pages 23-37 Oscillations in an Ensemble of Noninteracting Oscillators....Pages 39-47 Oscillations in Ordered Structures. Limit for a Continuous Medium Waves. Dispersion....Pages 49-79 Properties of Waves with Small Amplitudes in Continuous Media....Pages 81-120 Stability and Instability of Linear Systems with Discrete Spectra....Pages 121-140 Stability of Distributed Systems with Continuous Spectra....Pages 141-169 Propagation Velocity of Waves....Pages 171-184 Energy and Momentum of Waves....Pages 185-194 Waves with Negative Energy. Linked Waves....Pages 195-212 Parametric Systems and Parametric Instability....Pages 213-237 Adiabatic Invariants. Propagation of Waves in Inhomogeneous Media....Pages 239-272 The Nonlinear Oscillator....Pages 273-297 Periodic Self-Excited Oscillations....Pages 299-308 General Properties of Nonlinear Dynamic Systems in Phase Space....Pages 309-328 Self-Excited Oscillations in Multifrequency Systems....Pages 329-352 Resonance Interactions between Oscillators....Pages 353-374 Simple Waves and the Formation of Discontinuities....Pages 375-394 Stationary Shock Waves and Solitons....Pages 395-415 Modulated Waves in Nonlinear Media....Pages 417-443 Self-Excited Oscillations in Distributed Systems....Pages 445-463 Stochastic Dynamics in Simple Systems....Pages 465-501 The Onset of Turbulence....Pages 503-521 Self-Organization....Pages 523-536 Back Matter....Pages 537-577 'Et mai - ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost sheJf next to the dusty canister Iabclled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series
