Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new definition of rough paths on manifolds   Smooth manifolds are not the suitable context for trying to generalize the
concept of rough paths on a manifold. Indeed, when one is working with smooth
maps instead of Lipschitz maps and trying to solve a rough differential
equation, one loses the quantitative estimates controlling the convergence of
the Picard sequence. Moreover, even with a definition of rough paths in smooth
manifolds, ordinary and rough differential equations can only be solved locally
in such case. In this paper, we first recall the foundations of the Lipschitz
geometry, introduced in "Rough Paths on Manifolds" (Cass, T., Litterer, C. &
Lyons, T.), along with the main findings that encompass the classical theory of
rough paths in Banach spaces. Then we give what we believe to be a minimal
framework for defining rough paths on a manifold that is both less rigid than
the classical one and emphasized on the local behaviour of rough paths. We end
by explaining how this same idea can be used to define any notion of coloured
paths on a manifold.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
3
The categories of this paper are: physics
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph