Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear response for random dynamical systems   We study for the first time linear response for random compositions of maps,
chosen independently according to a distribution $\PP$. We are interested in
the following question: how does an absolutely continuous stationary measure
(acsm) of a random system change when $\PP$ changes smoothly to $\PP_{\eps}$?
For a wide class of one dimensional random maps, we prove differentiability of
acsm with respect to $\eps$; moreover, we obtain a linear response formula. We
apply our results to iid compositions, with respect to various distributions
$\PP_{\eps}$, of uniformly expanding circle maps, Gauss-R\'enyi maps (random
continued fractions) and Pomeau-Manneville maps. Our results yield an exact
formula for the invariant density of random continued fractions; while for
Pomeau-Manneville maps our results provide a precise relation between their
linear response under certain random perturbations and their linear response
under deterministic perturbations.

19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci