102 citations · 419 across the 36 of their papers we have counts for
7 papers · 1 filter
Number of limit cycles for planar systems with invariant algebraic curves
Armengol Gasull, Hector Giacomini
For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove n…
Effectiveness of the Bendixson-Dulac theorem
Armengol Gasull, Hector Giacomini
We illustrate with several new applications the power and elegance of the Bendixson Dulac theorem to obtain upper bounds of the number of limit cycles for several families of plana…
Solving polynomials with ordinary differential equations
Armengol Gasull, Hector Giacomini
In this work we consider a given root of a family of n-degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function sat…
A new approach for the study of limit cycles
J. D. García-Saldaña, A. Gasull, H. Giacomini
We prove that star-like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non-autonomous poly…
Some Applications of the Extended Bendixson-Dulac Theorem
Armengol Gasull, Hector Giacomini
During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of th…
Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems
Belen Garcia, Hector Giacomini, Jesus Perez del Rio
We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polyn…