Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbations of quadratic centers of genus one   We propose a program for finding the cyclicity of period annuli of quadratic
systems with centers of genus one. As a first step, we classify all such
systems and determine the essential one-parameter quadratic perturbations which
produce the maximal number of limit cycles. We compute the associated
Poincare-Pontryagin-Melnikov functions whose zeros control the number of limit
cycles. To illustrate our approach, we determine the cyclicity of the annuli of
two particular reversible systems.

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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th