Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adjoint-based variational method for constructing periodic orbits of
  high-dimensional chaotic systems   Chaotic dynamics in systems ranging from low-dimensional nonlinear
differential equations to high-dimensional spatio-temporal systems including
fluid turbulence is supported by non-chaotic, exactly recurring time-periodic
solutions of the governing equations. These unstable periodic orbits capture
key features of the turbulent dynamics and sufficiently large sets of orbits
promise a framework to predict the statistics of the chaotic flow. Computing
periodic orbits for high-dimensional spatio-temporally chaotic systems remains
challenging as known methods either show poor convergence properties because
they are based on time-marching of a chaotic system causing exponential error
amplification; or they require constructing Jacobian matrices which is
prohibitively expensive. We propose a new matrix-free method that is unaffected
by exponential error amplification, is globally convergent and can be applied
to high-dimensional systems. The adjoint-based variational method constructs an
initial value problem in the space of closed loops such that periodic orbits
are attracting fixed points for the loop-dynamics. We introduce the method for
general autonomous systems. An implementation for the one-dimensional
Kuramoto-Sivashinsky equation demonstrates the robust convergence of periodic
orbits underlying spatio-temporal chaos. Convergence does not require accurate
initial guesses and is independent of the period of the respective orbit.

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The categories of this paper are: chem-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs