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A note on analytic integrability of planar vector fields

Published online by Cambridge University Press:  23 April 2012

A. ALGABA ,
C. GARCÍA  and
M. REYES
A. ALGABA
Affiliation:
Department of Mathematics, Facultad de Ciencias Experimentales, Campus del Carmen, University of Huelva, Spain e-mail: [email protected], [email protected], [email protected]
C. GARCÍA
Affiliation:
Department of Mathematics, Facultad de Ciencias Experimentales, Campus del Carmen, University of Huelva, Spain e-mail: [email protected], [email protected], [email protected]
M. REYES
Affiliation:
Department of Mathematics, Facultad de Ciencias Experimentales, Campus del Carmen, University of Huelva, Spain e-mail: [email protected], [email protected], [email protected]
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Abstract

We give a new characterisation of integrability of a planar vector field at the origin. This allows us to prove that the analytic systems where h, K, Ψ and ξ are analytic functions defined in the neighbourhood of O with K(O) ≠ 0 or Ψ(O) ≠ 0 and n ≥ 1, have a local analytic first integral at the origin. We show new families of analytically integrable systems that are held in the above class. In particular, this class includes all the nilpotent and generalised nilpotent integrable centres that we know.

Keywords

First integralCentreSaddleMonodromic
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 5 , October 2012 , pp. 555 - 562
Copyright
Copyright © Cambridge University Press 2012

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