Rough integrators on Banach manifolds

Abstract

We introduce a notion of p-rough integrator on any Banach manifolds, for any $p\ge 1$, which plays the role of weak geometric Holder p-rough paths in the usual Banach space setting. The awaited results on rough differential equations driven by such objects are proved, and a canonical representation is given if the manifold is equipped with a connection.

13 pages, polished presentation