Shape index, Brouwer degree and Poincaré-Hopf theorem

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Sanjurjo, José M. R. and Barge Yáñez, Héctor (2023) Shape index, Brouwer degree and Poincaré-Hopf theorem. (Unpublished)

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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 Poincaré-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.


Item Type:Article
Uncontrolled Keywords:Shape index ; Brouwer degree ; Poincaré-Hopf theorem ; Non-saddle set
Subjects:Sciences > Mathematics > Topology
ID Code:77082
Deposited On:24 Mar 2023 15:19
Last Modified:24 Mar 2023 15:19

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