Name: Real analytic vector fields with first integral and separatrices
Keywords: first integral, 32S65, 37F75, 34Cxx, 14P15, Singularities of holomorphic vector fields and foliations, formal and analytic separatrix, FOS: Mathematics, Dynamical aspects of holomorphic foliations and vector fields, index of vector fields, Dynamical Systems (math.DS), real analytic vector field, reduction of singularities

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 Feb 2019Embargo end date: 01 Jan 2018 English Publisher:Springer Science and Business Media LLCJournal:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, volume 113, pages 4,031-4,049 (issn: 1578-7303, eissn: 1579-1505,

Authors: Rogério Mol; Fernando Sanz Sánchez;

doi: 10.1007/s13398-019-00639-y , 10.48550/arxiv.1805.05310

arXiv: http://arxiv.org/abs/1805.05310

Real analytic vector fields with first integral and separatrices

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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.

20 pages, 3 figures

Related Organizations

UNIVERSIDADE DE SAO PAULO
Brazil
Universidade Federal de Minas Gerais
Brazil
University of Valladolid
Spain

Keywords

first integral, 32S65, 37F75, 34Cxx, 14P15, Singularities of holomorphic vector fields and foliations, formal and analytic separatrix, FOS: Mathematics, Dynamical aspects of holomorphic foliations and vector fields, index of vector fields, Dynamical Systems (math.DS), real analytic vector field, reduction of singularities, Mathematics - Dynamical Systems

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