Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas
Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação)
Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques)
Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)

Date:	2017
Abstract:	Let QSH be the whole class of non-degenerate planar quadratic differential systems possessing at least one invariant hyperbola. We classify this family of systems, modulo the action of the group of real affine transformations and time rescaling, according to their geometric properties encoded in the configurations of invariant hyperbolas and invariant straight lines which these systems possess. The classification is given both in terms of algebraic geometric invariants and also in terms of affine invariant polynomials and it yields a total of 205 distinct such configurations. We have 162 configurations for the subclass QSH(η>0) of systems which possess three distinct real singularities at infinity, and 43 configurations for the subclass QSH(η=0) of systems which possess either exactly two distinct real singularities at infinity or the line at infinity filled up with singularities. The algebraic classification, based on the invariant polynomials, is also an algorithm which makes it possible to verify for any given real quadratic differential system if it has invariant hyperbolas or not and to specify its configuration of invariant hyperbolas and straight lines.
Grants:	European Commission 316338
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Affine invariant polynomials ; Algebraic solutions ; Configuration of algebraic solutions ; Group action ; Quadratic differential systems
Published in:	Electronic journal of differential equations, Vol. 2017, Issue 295 (2017) , p. 1-122, ISSN 1072-6691

Adreça alternativa: https://ejde.math.txstate.edu/Volumes/2017/295/oliveira.pdf

Postprint 129 p, 4.9 MB

122 p, 4.6 MB

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