Electrical network theory of countable graphs

The purpose of this dissertation is to derive the equations governing electrical networks of countable graphs and to give conditions assuring that these are gradient dynamical systems on semi-Riemannian Hilbert manifolds. Furthermore, we show how symmetries in the graph give rise to a G-action on the manifold of states. Finally, we present some mathematical results about gradient dynamical systems on semi-Riemannian Banach manifolds.