Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing general rough differential equations through flow
  approximations   The non-linear sewing lemma constructs flows of rough differential equations
from a braod class of approximations called almost flows. We consider a class
of almost flows that could be approximated by solutions of ordinary
differential equations, in the spirit of the backward error analysis. Mixing
algebra and analysis, a Taylor formula with remainder and a composition formula
are central in the expansion analysis. With a suitable algebraic structure on
the non-smooth vector fields to be integrated, we recover in a single framework
several results regarding high-order expansions for various kind of driving
paths. We also extend the notion of driving rough path. We also introduce as an
example a new family of branched rough paths, called aromatic rough paths
modeled after aromatic Butcher series.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn