4 papers
A sharp degree bound in the real Jacobian conjecture
F. Braun, J. Gwoździewicz, F. Fernandes +1
Let be a polynomial map with nowhere zero Jacobian determinant. A long-standing problem is to determine the largest integer such that the c…
Local and Global Analysis of the Displacement Map Some Near Integrable Systems
Francisco Braun, Leonardo da Cruz, Joan Torregrosa
In this paper, we introduce an alternative method for applying averaging theory of orders and in the plane. This is done by combining Taylor expansions of the displacement…
Bifurcations of polynomial functions with diffeomorphic fibers
Francisco Braun, Filipe Fernandes
The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than . In this note, the main res…
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…