Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Lindstedt series   The parametric equations of the surfaces on which highly resonant
quasi-periodic motions develop (lower-dimensional tori) cannot be analytically
continued, in general, in the perturbation parameter, i.e. they are not
analytic functions of the perturbation parameter. However rather generally
quasi-periodic motions whose frequencies satisfy only one rational relation
("resonances of order 1") admit formal perturbation expansions in terms of a
fractional power of the perturbation parameter, depending on the degeneration
of the resonance. We find conditions for this to happen, and in such a case we
prove that the formal expansion is convergent after suitable resummation.

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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: solv-int