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arXiv · 1309.5346

Limit cycles for a class of quintic $\mathbb{Z}_6-$equivariant systems without infinite critical points

Maria Jesus Álvarez·Isabel Salgado Labouriau·Adrian Calin Murza
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Abstract

We analyze the dynamics of a 4-parameter family of planar ordinary differential equations, given by a polynomial of degree 5 that is equivariant under a symmetry of order 6. We obtain the number of limit cycles as a function of the parameters, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points. The method used is the reduction of the problem to an Abel equation.

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Maria Jesus Álvarez, Isabel Salgado Labouriau, Adrian Calin Murza. 2014-10-29. Limit cycles for a class of quintic $\mathbb{Z}_6-$equivariant systems without infinite critical points. https://arxiv.org/abs/1309.5346

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