Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduced-order Description of Transient Instabilities and Computation of
  Finite-Time Lyapunov Exponents   High-dimensional chaotic dynamical systems can exhibit strongly transient
features. These are often associated with instabilities that have finite-time
duration. Because of the finite-time character of these transient events, their
detection through infinite-time methods, e.g. long term averages, Lyapunov
exponents or information about the statistical steady-state, is not possible.
Here we utilize a recently developed framework, the Optimally Time-Dependent
(OTD) modes, to extract a time-dependent subspace that spans the modes
associated with transient features associated with finite-time instabilities.
As the main result, we prove that the OTD modes, under appropriate conditions,
converge exponentially fast to the eigendirections of the Cauchy--Green tensor
associated with the most intense finite-time instabilities. Based on this
observation, we develop a reduced-order method for the computation of
finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems,
the computational cost of the reduced-order method is orders of magnitude lower
than the full FTLE computation. We demonstrate the validity of the theoretical
findings on two numerical examples.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph