Real Analytic Vector Fields with First Integral and Separatrices

Rogério Mol; Fernando Sanz Sánchez

Real Analytic Vector Fields with First Integral and Separatrices

Dynamical Systems 2018-05-15 v1

Authors: Rogério Mol , Fernando Sanz Sánchez

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.

Keywords

vector fields

Cite

@article{arxiv.1805.05310,
  title  = {Real Analytic Vector Fields with First Integral and Separatrices},
  author = {Rogério Mol and Fernando Sanz Sánchez},
  journal= {arXiv preprint arXiv:1805.05310},
  year   = {2018}
}

Comments

20 pages, 3 figures

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