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Time-reversibility and integrability of p:-q resonant vector fields
Jaume Gine, Valery G. Romanovski, Joan Torregrosa
We study local analytical integrability in a neighborhood of resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect…
Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line
Leonardo P. C. da Cruz, Joan Torregrosa
We solve the center-focus problem in a class of piecewise quadratic polynomial differential systems with an invariant straight line. The separation curve is also a straight line wh…
Limit cycles from a monodromic infinity in planar piecewise linear systems
Emilio Freire, Enrique Ponce, Joan Torregrosa +1
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and p…
A proof of Perko's conjectures for the Bogdanov-Takens system
Armengol Gasull, Hector Giacomini, Set Perez-Gonzalez +1
The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove…
Upper bounds for the number of zeroes for some Abelian integrals
Armengol Gasull, J. Tomás Lázaro, Joan Torregrosa
Consider the vector field where the set of critical points is formed by straight lines, not passing through the origin and paral…