Marcello Seri (Groningen)
Contact mechanics and numerical integration
It is well known that an analogue to Hamiltonian systems can be defined on contact manifolds, the odd dimensional cousins to the even symplectic manifold. Their odd dimensionality introduces an extra freedom that allows the energy to vary and which is not necessarily restricted to a time-dependence. In the talk, we will present some geometric integrators for contact Hamiltonian systems, numerical schemes that guarantee the the preservation of the contact geometric structure. The derivation of the numerical integrators will be used as way to review some of the most relevant properties of contact Hamiltonian systems and to provide some intriguing examples that motivated the recent surge of interest in their analytical and numerical study.