Title: ODEs on subCartesian spaces
Abstract: (this is joint work with Yael Karshon, in progress). SubCartesian spaces were introduced by Aronszajn in 1967. These are spaces locally modelled on (arbitrary!) subspaces of various R^n's. One can define vector fields on such spaces. The existence of integral curves of such vector fields was proved by Snyaticki around 2007. We are working on proving the smoothness of flows of vector fields on subCartesian spaces. We have a proof of smoothness in a number of useful special cases (the subCartesian space actually embeds in some R^N) and we are close to proving it in full generality.
