Título
Real analytic vector fields with first integral and separatrices
Documento Fuente
RACSAM, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, vol. 113 (4), 2019, 4031-4049
Résumé
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
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.
Propietario de los Derechos
Real Academia de Ciencias, España
Tipo de versión
info:eu-repo/semantics/acceptedVersion
Derechos
restrictedAccess
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