Real analytic vector fields with first integral and separatrices

Mol, Rogério; Sánchez, Fernando Sanz

doi:10.1007/s13398-019-00639-y

Por favor, use este identificador para citar o enlazar este ítem:https://uvadoc.uva.es/handle/10324/68130

Título

Real analytic vector fields with first integral and separatrices

Autor

Mol, Rogério

Sánchez, Fernando Sanz

Año del Documento

2019

Editorial

Springer

Documento Fuente

RACSAM, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, vol. 113 (4), 2019, 4031-4049

Abstract

We prove that a germ of analytic vector field at (R3, 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.

Palabras Clave

Real analytic vector eld, rst integral, formal and analytic separatrix, reduction of singularities, index of vector elds

ISSN

1578-7303

Revisión por pares

DOI

10.1007/s13398-019-00639-y

Patrocinador

First author partially supported by Pronex-Faperj, CNPq-Universal, CAPES-Mathamsud. Second author partially supported by Ministerio de Educaci on y Cultura, Spain, process MTM2013-46337-C2-1-P and MTM2016-77642-C2-1-P, and by Programa Hispano-Brasileño de Cooperación Interuniversitaria, process PHB2010-0122-PC.