RT Journal Article
T1 A note on analytic integrability of planar vector fields
A1 Algaba Durán, Antonio
A1 García García, Cristóbal
A1 Reyes Columé, Manuel
K1 Integrabilidad de sistemas diferenciales
AB We give a new characterisation of integrability of a planar vector field at the origin. This allows us to prove that the analytic systems ? = (?h/?y (x,y)K (h,y n) + y n-1 ?(h,y n) ?(x,y), ? = -?h/?x(x,y)K(h,y n) ?(x,y), where h, K, ? and ? are analytic functions defined in the neighbourhood of O with K(O) ? 0 or ?(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
PB Cambridge University Press
SN 10.1017/s0956792512000113
SN 0956-7925
SN 1469-4425 (electrónico)
YR 2012
FD 2012-10
LK https://hdl.handle.net/10272/25455
UL https://hdl.handle.net/10272/25455
LA eng
NO ALGABA, A., GARCÍA, C., & REYES, M. (2012). A note on analytic integrability of planar vector fields. European Journal of Applied Mathematics, 23(5), 555–562. https://doi.org/10.1017/s0956792512000113
NO This work has been partially supported by  Ministerio deCiencia e Innovación, co-financed withFEDER funds, in the frame of the project MTM2010-20907-C02-02 and by Consejería de Educación y Ciencia de la Junta deAndalucía (FQM-276 and EXC/2008/FQM-872)
DS Repositorio Institucional de la Universidad de Huelva
RD 1 jun 2026