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arXiv · 1805.05310

Real Analytic Vector Fields with First Integral and Separatrices

Rogério Mol·Fernando Sanz Sánchez
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Abstract

We prove that a germ of analytic vector field at $(\mathbb{R}^3,0)$ that possesses a non-constant analytic first integral has a real formal separatrix. We provide an example which shows that such a vector field does not necessarily have a real analytic separatrix.

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Rogério Mol, Fernando Sanz Sánchez. 2018-05-14. Real Analytic Vector Fields with First Integral and Separatrices. https://arxiv.org/abs/1805.05310

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