Bifurcation of polynomials, index of the gradient at infinity, and applications (Main title: Index of the gradient at infinity and Bifurcation locus)

• Grant number: 20/14111-2
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: October 01, 2021
• End date: September 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Raimundo Nonato Araújo dos Santos
• Grantee: Gabriel Esteban Perico Monsalve
• Supervisor: Mihai Marius Tibar
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Université Lille 1 - Sciences et Technologies, France
• Associated to the scholarship: 19/24377-2 - Index of the gradient at infinity and bifurcation locus, BP.DR

Abstract

In this project we study the bifurcation locus of a polinomial function $ f : R^2 \to R$ and other phenomena at infinity as polar curves, bifurcation locus in families of curves, fibrations structures at infinity, curvature of fibres of polynomials, Gauss-Bonnet defect and Poincaré-Hopf type formula. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MONSALVE, GABRIEL E.. Atypical Values and the Milnor Set of Real Polynomials in Two Variables. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 54, n. 1, p. 19-pg., 2023-03-01. (19/24377-2, 20/14111-2)