Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant manifolds for stochastic partial differential equations   Invariant manifolds provide the geometric structures for describing and
understanding dynamics of nonlinear systems. The theory of invariant manifolds
for both finite and infinite dimensional autonomous deterministic systems, and
for stochastic ordinary differential equations is relatively mature. In this
paper, we present a unified theory of invariant manifolds for infinite
dimensional {\em random} dynamical systems generated by
  {\em stochastic} partial differential equations. We first introduce a random
graph transform and a fixed point theorem for non-autonomous systems. Then we
show the existence of generalized fixed points which give the desired invariant
manifolds.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int