The classical notion of retraction map used to approximate geodesics is extended and
rigorously defined to become a powerful tool to construct geometric integrators and it is …

Geometric mechanics is a fairly recent field of mathematics lying in the intersection of at least
four different scientific fields: differential geometry, physics, numerical analysis and …

Similar to the case of Riemannian geodesics, one may define conjugate points for systems
of second-order ordinary differential equations (SODEs). In this dissertation we provide a …

The classical notion of retraction map used to approximate geodesics is extended and
rigorously defined to become a powerful tool to construct geometric integrators. Using the …