Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A dynamical system associated with the fixed points set of a
  nonexpansive operator   We study the existence and uniqueness of (locally) absolutely continuous
trajectories of a dynamical system governed by a nonexpansive operator. The
weak convergence of the orbits to a fixed point of the operator is investigated
by relying on Lyapunov analysis. We show also an order of convergence of
$o(\frac{1}{\sqrt{t}})$ for the fixed point residual of the trajectory of the
dynamical system. We apply the results to dynamical systems associated with the
problem of finding the zeros of the sum of a maximally monotone operator and a
cocoercive one. Several dynamical systems from the literature turn out to be
particular instances of this general approach.

8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th