Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isochronicity conditions for some real polynomial systems   This paper focuses on isochronicity of linear center perturbed by a
polynomial. Isochronicity of a linear center perturbed by a degree four and
degree five polynomials is studied, several new isochronous centers are found.
For homogeneous isochronous perturbations, a first integral and a linearizing
change of coordinates are presented. Moreover, a family of Abel polynomial
systems is also considered. By investigations until degree 10 we prove the
existence of a unique isochronous center. These results are established using a
computer implementation based on Urabe theorem.

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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci