Half a Century with the Problem of the Gradient of an Analytic Function

Fernando Sanz Sánchez ()
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Fernando Sanz Sánchez: University of Valladolid, Departamento de Álgebra, Análisis Matemático, Geometría y Topología

Chapter Chapter 7 in Handbook of Geometry and Topology of Singularities V: Foliations, 2024, pp 335-395 from Springer

Abstract: Abstract This is a review concerning the study of the local dynamics of a gradient vector field of a real analytic function. Starting from the famous Thom’s Gradient Conjecture, we discuss the state of art of the Finiteness Conjecture on non-oscillation of trajectories and we end with the formulation of the problem in the context of o-minimal geometry.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-52481-3_7

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DOI: 10.1007/978-3-031-52481-3_7

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