Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal time averages in non-autonomous nonlinear dynamical systems   The auxiliary function method allows computation of extremal long-time
averages of functions of dynamical variables in autonomous nonlinear ordinary
differential equations via convex optimization. For dynamical systems defined
by autonomous polynomial vector fields, it is operationally realized as a
semidefinite program utilizing sum of squares technology. In this contribution
we review the method and extend it for application to periodically driven
non-autonomous nonlinear vector fields involving trigonometric functions of the
dynamical variables. The damped driven Duffing oscillator and periodically
driven pendulum are presented as examples to illustrate the auxiliary function
method's utility.

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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con