The classical Poincaré–Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than 1.
Titolo: | On the topological degree of planar maps avoiding normal cones |
Autori: | |
Data di pubblicazione: | 2019 |
Stato di pubblicazione: | Pubblicato |
Rivista: | |
Abstract: | The classical Poincaré–Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than 1. |
Handle: | http://hdl.handle.net/11368/2945969 |
Digital Object Identifier (DOI): | 10.12775/TMNA.2019.034 |
URL: | https://apcz.umk.pl/czasopisma/index.php/TMNA/article/view/TMNA.2019.034 |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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