Tapia, NikolasZambotti, Lorenzo2020-12-162020-12-162020-03-180024-6115https://depositonce.tu-berlin.de/handle/11303/12202http://dx.doi.org/10.14279/depositonce-11077We construct an explicit transitive free action of a Banach space of Hölder functions on the space of branched rough paths, which yields in particular a bijection between these two spaces. This endows the space of branched rough paths with the structure of a principal homogeneous space over a Banach space and allows to characterize its automorphisms. The construction is based on the Baker–Campbell–Hausdorff formula, on a constructive version of the Lyons–Victoir extension theorem and on the Hairer–Kelly map, which allows to describe branched rough paths in terms of anisotropic geometric rough paths.en510 Mathematik60H10 (primary)16T05 (secondary)Article2020-12-071460-244X