RT Journal Article
T1 Characterizing isochronous points and computing isochronous sections
A1 Algaba Durán, Antonio
A1 Reyes Columé, Manuel
AB We consider two-dimensional autonomous systems of differentialequations$$\dot{x}=-y+\lambda x+P(x,y),\qquad \dot{y}=x+\lambda y+Q(x,y),$$where $\lambda$ is a real constant and $P$ and $Q$ are smoothfunctions of order greater than or equal to two. These systems,so-called centre-focus type systems, have either a centre or afocus at the origin.  We characterize the systems with a weakisochronous focus at the origin by means of their radial andazimuthal coefficients. We prove, in this case, the existence of anormalized vector field and an  isochronous section which arrivesat the origin with defined direction. We also provide algorithmsthat compute the radial and azimuthal coefficients, terms ofnormalized vector field and of isochronous section of a system. Asapplications, we analyze the weak isochronous foci for quadraticsystems and for systems with cubic non-linearities, and we give athree-parameter family of Rayleigh equations with four localcritical periods.
PB Elsevier
SN 0022-247X
SN 1096-0813 (electrónico)
YR 2009
FD 2009-07-15
LK https://hdl.handle.net/10272/25431
UL https://hdl.handle.net/10272/25431
LA eng
NO Algaba, A., & Reyes, M. (2009). Characterizing isochronous points and computing isochronous sections. In Journal of Mathematical Analysis and Applications (Vol. 355, Issue 2, pp. 564–576). Elsevier BV. https://doi.org/10.1016/j.jmaa.2009.02.007
NO This work has been partially supported by  Ministerio deCiencia y Tecnología, Plan Nacional I+D+I co-financed withFEDER funds, in the frame of the project MTM2007-64193 and by Consejería de Educación y Ciencia de la Junta deAndalucía (FQM-276 and EXC/2008)
DS Repositorio Institucional de la Universidad de Huelva
RD 1 jun 2026