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Isochronicity and Commutation of Polynomial Vector Fields

E. P. Volokitin·V. V. Ivanov
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Abstract

We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and constructive description of centralizers of the Abel polynomial systems. We give new examples of isochronous systems.

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E. P. Volokitin, V. V. Ivanov. 1999-09-16. Isochronicity and Commutation of Polynomial Vector Fields. https://arxiv.org/abs/math/9909091

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