39 citations · 97 across the 9 of their papers we have counts for
7 papers · 1 filter
Atypical points at infinity and algorithmic detection of the bifurcation locus of real polynomials
Luis Renato G. Dias, Cezar Joiţa, Mihai Tibăr
We show that the variation of the topology at infinity of a two-variable polynomial function is localisable at a finite number of "atypical points" at infinity. We construct an eff…
On Topological Approaches to the Jacobian Conjecture in
Francisco Braun, Luis Renato G. Dias, Jean Venato-Santos
We obtain a structure theorem for the nonproperness set of a nonsingular polynomial mapping . Jelonek's results on and our result show…
Towards effective detection of the bifurcation locus of real polynomial maps
Luis Renato G. Dias, Susumu Tanabé, Mihai Tibar
We answer to a problem raised by recent work of Jelonek and Kurdyka: how can one detect by rational arcs the bifurcation locus of a polynomial map $\bR^n\to\bR^p$ in case . We…
Detecting bifurcation values at infinity of real polynomials
Luis Renato G. Dias, Mihai Tibar
We present a new approach for estimating the set of bifurcation values at infinity. This yields a significant shrinking of the number of coefficients in the recent algorithm introd…
Invertible polynomial mappings via Newton non-degeneracy
Ying Chen, L. R. G. Dias, Kiyoshi Takeuchi +1
We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a ma…
On Newton non-degeneracy of polynomial mappings
Y. Chen, L. R. G. Dias, M. Tibar
We introduce a new non-degeneracy condition at infinity for a real or a mixed polynomial mapping which allows us to approximate its bifurcation locus in terms of certain Newton…
Regularity at infinity of real mappings and a Morse-Sard theorem
L. R. G. Dias, M. A. S. Ruas, M. Tibar
We prove a new Morse-Sard type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for mappings. We show the equival…