Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant manifolds for random and stochastic partial differential
  equations   Random invariant manifolds are geometric objects useful for understanding
complex dynamics under stochastic influences. Under a nonuniform hyperbolicity
or a nonuniform exponential dichotomy condition, the existence of random
pseudo-stable and pseudo-unstable manifolds for a class of \emph{random}
partial differential equations and \emph{stochastic} partial differential
equations is shown. Unlike the invariant manifold theory for stochastic
\emph{ordinary} differential equations, random norms are not used. The result
is then applied to a nonlinear stochastic partial differential equation with
linear multiplicative noise.

26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol