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22 p, 716.4 KB

Generalized rational first integrals of analytic differential systems / Cong, Wang (Shanghai Jiaotong University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincaré's one [16], the Furta's one [8], part of Chen et al's ones [4], and the Shi's one [18]. [...]
2011 - DOI (Digital Object Identifier)

10.1016/j.jde.2011.05.016
Journal of differential equations, Vol. 251 (2011) , p. 2770-2788

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13 p, 342.5 KB

The index of singularities of vector fields and finite jets / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Saghin, Radu (Universitat Autònoma de Barcelona. Centre de Recerca per a l'Educació Científica i Matemàtica)
We describe when the index of a singularity of a smooth vector field is determined by a finite jet at the singularity. We also give some criteria to determine some terms from the formal series expansion of the vector field at the singularity which determine the index.
2011 - DOI (Digital Object Identifier)

10.1016/j.jde.2011.04.015
Journal of differential equations, Vol. 251 (2011) , p. 2822-2832

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