Gradient versus proper gradient homotopies

2019/10/28 by Bartłomiejczyk, Piotr, Nowak-Przygodzki, Piotr
#55M25 (Secondary) #55Q05 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.12568

Abstract

We compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classifications are essentially different. We provide a complete description of the sets of homotopy classes of gradient maps from ℝⁿ to ℝⁿ and proper gradient maps from ℝ² to ℝ² with the Brouwer degree greater or equal to zero.

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