Francisco Braun

activity

20142026

most citedZero-Hopf bifurcation in a 3-D jerk system

23 citations · 56 across the 9 of their papers we have counts for

collaborators

10 papers

math.GT2026

Two non-semisimple quantum invariants of lens spaces

Rhea Palak Bakshi, Mitchell Jubeir, Quinn T. Kolt

We calculate the chromatic spherical invariant $K_{Rep (H)} (L (p, q))$ of lens spaces $L (p, q)$ for arbitrary finite-dimensional unibalanced, unimodular Hopf algebr…

math.DS2022

Topological equivalence of submersion functions and topological equivalence of their foliations on the plane: the linear-like case

Francisco Braun, Ingrid S. Meza-Sarmiento

Let $f, g : R^{2} \to R$ be two submersion functions and $F (f)$ and $F (g)$ be the regular foliations of $R^{2}$ whose leaves are the conne…

math.GT2021★ 1 cited

Surjectivity of linear operators and semialgebraic global diffeomorphisms

Francisco Braun, Luis Renato Gonçalves Dias, Jean Venato Santos

We prove that a $C^{\infty}$ semialgebraic local diffeomorphism of $R^{n}$ with non-properness set having codimension greater than or equal to $2$ is a global diffeomorphism…

math.GT2020★ 3 cited

On global invertibility of semi-algebraic local diffeomorphisms

Francisco Braun, Luis Renato Gonçalves Dias, Jean Venato-Santos

In this partly expository paper we discuss conditions for the global injectivity of $C^{2}$ semi-algebraic local diffeomorphisms $f : R^{n} \to R^{n}$ . In case $n > 2$ , w…

math.DS2020★ 23 cited

Zero-Hopf bifurcation in a 3-D jerk system

Francisco Braun, Ana C. Mereu

We consider the 3-D system defined by the jerk equation $x ... = - a x ¨ + x x ˙^{2} - x^{3} - b x + c x ˙$ , with $a, b, c \in R$ . When $a = b = 0$ and $c < 0$ the eq…

math.CV2020

A canonical embedding of $Aut_{hol} (C^{n})$

Francisco Braun, Frederico Xavier

The group $Aut_{hol} (C^{n})$ of self-biholomorphisms of $C^{n}$ consists of affine maps if $n = 1$ , but in higher dimensions it is a large object that has n…

math.AG2018

On Topological Approaches to the Jacobian Conjecture in $C^{n}$

Francisco Braun, Luis Renato G. Dias, Jean Venato-Santos

We obtain a structure theorem for the nonproperness set $S_{f}$ of a nonsingular polynomial mapping $f : C^{n} \to C^{n}$ . Jelonek's results on $S_{f}$ and our result show…

math.DS2017★ 1 cited

On the connection between global centers and global injectivity in the plane

Francisco Braun, Jaume Llibre

In this note we present a generalization of a result of Sabatini relating global injectivity and global centers. The shape of the image of the map is taking into account. Our proof…

math.DS2016★ 7 cited

Foliations, solvability and global injectivity

Francisco Braun, José Ruidival dos Santos Filho, Marco Antonio Teixeira

Let $F : R^{n} \to R^{n}$ be a $C^{\infty}$ map such that $D F (x)$ is invertible for every $x \in R^{n}$ . Although being a local diffeomorphism, $F$ is not necessari…

math.DS2014★ 21 cited

On polynomial submersions of degree $4$ and the real Jacobian conjecture in $R^{2}$

F. Braun, B. Oréfice-Okamoto

The main result of this paper is the following version of the real Jacobian conjecture: "Let $F = (p, q) : R^{2} \to R^{2}$ be a polynomial map with nowhere zero Jacobian determinant. If th…