Rough integrators on Banach manifolds

Ismaël Bailleul (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We introduce a notion of p-rough integrator on any Banach manifolds, for any $p\geq 1$, 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.

Domaines: Analyse classique [math.CA]; Géométrie différentielle [math.DG]

Ismaël Bailleul. Rough integrators on Banach manifolds. Bulletin des Sciences Mathématiques, 2019, 151, pp.51-65. ⟨10.1016/j.bulsci.2018.12.001⟩. ⟨hal-00979559⟩