TimeDependentHarmonicOscillators 2009-05-29 13:46:17 2009-05-29 13:46:17 Topic Ermakov systems time-dependent harmonic oscillators \section{Time-dependent harmonic oscillators} Nonlinear equations are of increasing interest in Physics. One of the simplest examples is called Milne--Pinney equation: \subsection{Ermakov systems} This equation was introduced in the nineteenth century by V.P. Ermakov, as a way of looking for a first integral for the time-dependent harmonic oscillator. He employed some of Lie's ideas for dealing with ordinary differential equations with the tools of classical geometry. Lie had previously obtained a characterisation of non-autonomous systems of first-order differential equations admitting a superposition rule. \textbf{[More to come]}