Index of the gradient at infinity and bifurcation locus

• Grant number: 19/24377-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2020
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Raimundo Nonato Araújo dos Santos
• Grantee: Gabriel Esteban Perico Monsalve
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 20/14111-2 - Bifurcation of polynomials, index of the gradient at infinity, and applications (Main title: Index of the gradient at infinity and Bifurcation locus), BE.EP.DR

Abstract

In this project we study the bifurcation locus of a polinomial function f:R^2 -- R and other phenomena at infinity as polar curves, bifurcation locus in families of curves, fibration structures at infinity, curvature of the fibres at infinity, 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MONSALVE, Gabriel Esteban Perico. Bifurcation set and index at infinity of polynomials. 2023. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.