102 citations · 419 across the 36 of their papers we have counts for
37 papers
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…
Frustration -- Exactly Solved Frustrated Models
H. T. Diep, H. Giacomini
After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex mo…
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…
Inflationary models that generalize the constant roll constraint
B. Boisseau, H. Giacomini
Recently a class of inflationary models satisfying the constant rate of roll constraint, , has been studied and compared with the latest cosmological observat…