Analytic normalization of analytically integrable differential systems near a periodic orbit

Kesheng Wu; Xiang Zhang

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Analytic normalization of analytically integrable differential systems near a periodic orbit

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arxiv 1407.7944 v1 pith:YYOLQNXU submitted 2014-07-30 math.CA math.DS

Analytic normalization of analytically integrable differential systems near a periodic orbit

Kesheng Wu , Xiang Zhang This is my paper

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For an analytic differential system in $\mathbb R^n$ with a periodic orbit, we will prove that if the system is analytically integrable around the periodic orbit, i.e. it has $n-1$ functionally independent analytic first integrals defined in a neighborhood of the periodic orbit, then the system is analytically equivalent to its Poincar\'e--Dulac type normal form. This result is an extension for analytic integrable differential systems around a singularity to the ones around a periodic orbit.

Analytic normalization of analytically integrable differential systems near a periodic orbit

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