Shape index, Brouwer degree and Poincar\'e-Hopf theorem
Dynamical Systems
2024-01-17 v2
Abstract
In this paper we study the relationship of the Brouwer degree of a vector field with the dynamics of the induced flow. Analogous relations are studied for the index of a vector field. We obtain new forms of the Poincar% \'{e}-Hopf theorem and of the Borsuk and Hirsch antipodal theorems. As an application, we calculate the Brouwer degree of the vector field of the Lorenz equations in isolating blocks of the Lorenz strange set.
Keywords
Cite
@article{arxiv.2303.06472,
title = {Shape index, Brouwer degree and Poincar\'e-Hopf theorem},
author = {Héctor Barge and José M. R. Sanjurjo},
journal= {arXiv preprint arXiv:2303.06472},
year = {2024}
}