ABSTRACT
The oscillator is a key concept in physics and other branches of science because the motion of single and coupled oscillators close to their oscillation threshold can be described in a universal way. Nonlinear oscillators can be classified according the sign of their damping coefficient. Spatially distributed oscillators and their perturbations can be treated in a similar way. The equations which describe the time evolution of the amplitude of the oscillation are known as normal form and can be derived using tools borrowed from singularity theory or by using more classical techniques belonging to singular perturbation theory. It has been argued that the normal form is valid only close to the threshold, that is when the non-linear effects are weak. The chapter discusses the normal form description of simple oscillators with and without any dissipation or external force. It is devoted to the problem of spatially distributed equations.
