6 papers
A family of Hurwitz polynomial vector fields in having non-constant periodic orbits
Álvaro Castañeda, Salomón Rebollo-Perdomo
We construct a two-parameter family of polynomial vector fields in and prove that, on a nonempty open set of parameter values, every member of the family is Hurwitz…
A family of planar Lotka--Volterra systems with invariant algebraic curves of arbitrary degree
Javier Coyo-Guarachi, Salomón Rebollo-Perdomo
We introduce a new family of planar Lotka--Volterra systems admitting explicit invariant algebraic curves of arbitrarily high degree.
Abelian integrals for polynomials with trivial global monodromy on
Jesús Muciño-Raymundo, Salomón Rebollo-Perdomo
We consider infinitesimal perturbations of Hamiltonian differential equations on the complex plane , where is a polynomial of degree …
Discrete and continuous dynamics of real -dimensional nilpotent polynomial vector fields
Álvaro Castañeda, Salomón Rebollo-Perdomo
A large class of real -dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete an…
Addition theorems for Ck real functions and applications in ordinary differential equations
Francisco Crespo, Salomón Rebollo-perdomo, Jorge L. Zapata
This work establishes the existence of addition theorems and double-angle formulas for Ck real scalar functions. Moreover, we determine necessary and sufficient conditions for a bi…
The number of medium amplitude limit cycles of some generalized Liénard systems
Salomón Rebollo-Perdomo
We will consider two special families of polynomial perturbations of the linear center. For the resulting perturbed systems, which are generalized Liénard systems, we provide the e…