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Noether's theorem and first integrals of ordinary differential equations.
The Lie theory of extended groups is a practical tool in the analysis of differential equations, particularly in the construction of solutions. A formalism of the Lie theory is given and contrasted with Noether's theorem ...
Algebraic properties of ordinary differential equations.
In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first ...
Ermakov systems : a group theoretic approach.
The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) ...
Lie symmetries of junction conditions for radiating stars.
We consider shear-free radiating spherical stars in general relativity. In particular we study the junction condition relating the pressure to the heat flux at the boundary of the star. This is a nonlinear equation in ...