Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract integration, Combinatorics of Trees and Differential Equations   This is a review paper on recent work about the connections between rough
path theory, the Connes-Kreimer Hopf algebra on rooted trees and the analysis
of finite and infinite dimensional differential equation. We try to explain and
motivate the theory of rough paths introduced by T. Lyons in the context of
differential equations in presence of irregular noises. We show how it is used
in an abstract algebraic approach to the definition of integrals over paths
which involves a cochain complex of finite increments. In the context of such
abstract integration theories we outline a connection with the combinatorics of
rooted trees. As interesting examples where these ideas apply we present two
infinite dimensional dynamical systems: the Navier-Stokes equation and the
Korteweg-de-Vries equation.

11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci