Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Angular values of nonautonomous and random linear dynamical systems   We introduce the notion of angular values for nonautonomous linear difference
equations and random linear cocycles. We measure the principal angles between
subspaces of fixed dimension as they evolve under nonautonomous or random
linear dynamics. The focus is on long-term averages of these principal angles,
which we call angular values: we demonstrate relationships between different
types of angular values and prove their existence for random dynamical systems.
For one-dimensional subspaces in two-dimensional systems our angular values
agree with the classical theory of rotation numbers for orientation-preserving
circle homeomorphisms if the matrix has positive determinant and does not
rotate vectors by more than $\frac{\pi}{2}$. Because our notion of angular
values ignores orientation by looking at subspaces rather than vectors, our
results apply to dynamical systems of any dimension and to subspaces of
arbitrary dimension. We treat angular values in the nontrivial autonomous case
in detail and show how angular values may be obtained from generalized
eigenspaces. This leads to a numerical algorithm for computing angular values
via Schur decompositions.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess