We present a short history of the Ermakov Equation with an emphasis on its discovery by the
West and the subsequent boost to research into invariants for nonlinear systems although …

Lie systems form a class of systems of first-order ordinary differential equations whose
general solutions can be described in terms of certain finite families of particular solutions …

Understanding the non-equilibrium quantum dynamics of many-body systems is one of the
most challenging problems in modern theoretical physics. While numerous approximate and …

We present a brief overview of classical isochronous planar differential systems focusing
mainly on the second equation of the Liénard type ẍ+ f (x) ẋ2+ g (x)= 0. In view of the close …

A new form to construct complex superpotentials that produce real energy spectra in
supersymmetric quantum mechanics is presented. This is based on the relation between the …

Abstract We study Lie–Hamilton systems on the plane, ie systems of first-order differential
equations describing the integral curves of a t-dependent vector field taking values in a finite …

This work concerns the definition and analysis of a new class of Lie systems on Poisson
manifolds enjoying rich geometric features: the Lie–Hamilton systems. We devise methods …

A Lie system is a non-autonomous system of first-order differential equations possessing a
superposition rule, ie a map expressing its general solution in terms of a generic finite family …

We use the geometric approach to the theory of Lie systems of differential equations in order
to study dissipative Ermakov systems. We prove that there is a superposition rule for …

Superposition rules form a class of functions that describe general solutions of systems of
first-order ordinary differential equations in terms of generic families of particular solutions …