F. Fernandes

activity

20192026

collaborators

5 papers

math.AG2026

A sharp degree bound in the real Jacobian conjecture

F. Braun, J. Gwoździewicz, F. Fernandes +1

Let $F = (p, q) : R^{2} \to R^{2}$ be a polynomial map with nowhere zero Jacobian determinant. A long-standing problem is to determine the largest integer $k$ such that the c…

math.AG2025

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 $1$ . In this note, the main res…

math.AG2023

The PInchuk example revisited

Filipe Fernandes, Zbigniew Jelonek

In this note we provide two special examples of non-injective polynomial maps from $R^{2}$ to $R^{2}$ with non-vanishing Jacobian: the first one is surjective, the se…

math.AG2020

A new class of non-injective polynomial local diffeomorphisms on the plane

Filipe Fernandes

In this short note we provide the example with the lowest degree known so far of a non-injective local polynomial diffeomorphism $F = (p, q) : R^{2} \to R^{2}$ . In our exa…

math.DS2019

A switched server system semi-conjugate to a minimal interval exchange

Filipe Fernandes, Benito Pires

Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typica…