64 citations · 81 across the 10 of their papers we have counts for
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Weak-Coppel problem for a class of Riccati differential equations
Armengol Gasull, Douglas D. Novaes, Joan Torregrosa
We study the -periodic solutions of the real Riccati differential equation where and is a -periodic function. Our goal is to define a real-val…
On the number of limit cycles in piecewise planar quadratic differential systems
Francisco Braun, Leonardo P. C. da Cruz, Joan Torregrosa
We consider piecewise quadratic perturbations of centers of piecewise quadratic systems in two zones determined by a straight line through the origin. By means of expansions of the…
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…
New lower bound for the Hilbert number in piecewise quadratic differential systems
Leonardo P. C. da Cruz, Douglas D. Novaes, Joan Torregrosa
We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line.…
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…
Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations
Hector Giacomini, Armengol Gasull, Joan Torregrosa
It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic…
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…
Some results on homoclinic and heteroclinic connections in planar systems
Armengol Gasull, Hector Giacomini, Joan Torregrosa
Consider a family of planar systems depending on two parameters and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclin…