Mathematics

The aim of this talk is to provide some boundary conditions, based on the idea of inward-/outwardness, that allow to characterize vector fields with topological degree possibly different from 0 and ±1. This is obtained through some intuitive constructions that progressively generalize the Poincaré-Miranda's Theorem. Finally we apply the main result to the gradient field near a degenerate multi-saddle point.

This seminar is part of the AJS series of seminars.