Web of Science: 2 citas, Scopus: 2 citas, Google Scholar: citas
Global topological configurations of singularities for the whole family of quadratic differential systems
Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques)
Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)

Fecha: 2020
Resumen: In Artés et al. (Geometric configurations of singularities of planar polynomial differential systems. A global classification in the quadratic case. Birkhäuser, Basel, 2019) the authors proved that there are 1765 different global geometrical configurations of singularities of quadratic differential systems in the plane. There are other 8 configurations conjectured impossible, all of them related with a single configuration of finite singularities. This classification is completely algebraic and done in terms of invariant polynomials and it is finer than the classification of quadratic systems according to the topological classification of the global configurations of singularities, the goal of this article. The long term project is the classification of phase portraits of all quadratic systems under topological equivalence. A first step in this direction is to obtain the classification of quadratic systems under topological equivalence of local phase portraits around singularities. In this paper we extract the local topological information around all singularities from the 1765 geometric equivalence classes. We prove that there are exactly 208 topologically distinct global topological configurations of singularities for the whole quadratic class. The 8 global geometrical configurations conjectured impossible do not affect this number of 208. From here the next goal would be to obtain a bound for the number of possible different phase portraits, modulo limit cycles.
Nota: Número d'acord de subvenció MINECO/MTM2016-77278-P
Nota: Número d'acord de subvenció AGAUR/2017/SGR-1617
Nota: Número d'acord de subvenció EC/H2020/777911
Derechos: Tots els drets reservats.
Lengua: Anglès
Documento: article ; recerca ; acceptedVersion
Materia: Quadratic vector fields ; Infinite and finite singularities ; Affine invariant polynomials ; Poincaré compactification ; Configuration of singularities ; Topological equivalence relation
Publicado en: Qualitative Theory of Dynamical Systems, Vol. 19, Issue 1 (April 2020) , art. 51, ISSN 1662-3592

DOI: 10.1007/s12346-020-00372-7


Disponible a partir de: 2021-04-30
Postprint

El registro aparece en las colecciones:
Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
Artículos > Artículos de investigación
Artículos > Artículos publicados

 Registro creado el 2020-04-15, última modificación el 2020-08-01



   Favorit i Compartir