Global injectivity for applications between euclidean spaces

Author(s)

Yuri Cândido da Silva Ribeiro

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2007-11-19

Examining board members

Carlos Teobaldo Gutierrez Vidalon; Carlos Biasi; Francesco Mercuri

• Advisor: Carlos Teobaldo Gutierrez Vidalon

Abstract

We present some results which give suficient conditions for a local diffeomorphism from the n-dimensional Euclidean space into itself be globally injective. Within this context, we consider some partial results addressed to solve the well known Fixed Point Conjecture and Jacobian Conjecture. From the dynamical point of view, there are connections between global injectivity and global asymptotic stability. In this way, we present a solution of the Markus-Yamabe Conjecture and of the LaSalle Problem (AU)