We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, theâ€¦ (More)

Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.

A powerful method to solve nonlinear first-order ordinary differential equations, which is based on a geometrical understanding of the corresponding dynamics of the so-called Lie systems, isâ€¦ (More)

The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular, Riccati equations and Ermakov systems. Manyâ€¦ (More)

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 solutions of suchâ€¦ (More)

Time-dependent frequency harmonic oscillators (TDFHOâ€™s) are studied through the theory of Lie systems. We show that they are related to a certain kind of equations in the Lie group SL(2,R). Someâ€¦ (More)

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent SchrÃ¶dinger equations of Lie typeâ€¦ (More)

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. Asâ€¦ (More)

A Lie system is a nonautonomous system of first-order differential equations admitting a superposition rule, i.e., a map expressing its general solution in terms of a generic family of particularâ€¦ (More)

A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into membersâ€¦ (More)