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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 type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): October 01, 2021
Effective date (End): September 30, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Raimundo Nonato Araújo dos Santos
Grantee:Gabriel Esteban Perico Monsalve
Supervisor abroad: Mihai Marius Tibar
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: 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)

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