Twin polynomial vector fields of arbitrary degree
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)

Data:	2022
Resum:	In this paper we study polynomial vector fields on C2 of degree larger than 2 with n2 isolated singularities. More precisely, we show that if two polynomial vector fields share n2−1 singularities with the same spectra (trace and determinant) and from these singularities n2−2 have the same positions, then both vector fields have identical position and spectra at all the singularities. Moreover we also show that if two polynomial vector fields share n2−1 singularities with the same positions and from these singularities n2−2 have the same spectra, then both vector fields have identical position and spectra at all the singularities. Moreover we also prove that generic vector fields of degree n>2 have no twins and that for any n>2 there exist two uniparametric families of twin vector fields, i. e. two different families of vector fields having exactly the same singular points and for each singular point both vector fields have the same spectrum.
Ajuts:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Euler-Jacobi formula ; Singular points ; Topological index ; Polynomial differential systems ; Berlinskii's Theorem
Publicat a:	Bulletin of the Brazilian Mathematical Society, Vol. 53, Issue 1 (March 2022) , p. 295-306, ISSN 1678-7544

DOI: 10.1007/s00574-021-00259-4

Postprint 11 p, 285.4 KB

El registre apareix a les col·leccions:
Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
Articles > Articles publicats