Quadratic Planar Differential Systems with Algebraic Limit Cycles via Quadratic Plane Cremona Maps

Autor:	Alberich-Carramiñana, Maria, Ferragut, Antoni, Llibre, Jaume
Rok vydání:	2019
Předmět:	Mathematics - Dynamical Systems Mathematics - Algebraic Geometry 34A05 34A34 34C05
Druh dokumentu:	Working Paper
Popis:	In this paper we show how we can transform quadratic systems into new quadratic systems after some kind of birational transformations, the quadratic plane Cremona maps. We afterwards apply these transformations to the families of quadratic differential systems having an algebraic limit cycle. As a consequence, we provide a new family of quadratic systems having an algebraic limit cycle of degree 5. Moreover we show how the known families of quadratic differential systems having an algebraic limit cycle of degree greater than four are obtained using these transformations. We also provide the phase portraits on the Poincar\'e disk of all the families of quadratic differential systems having algebraic limit cycles. Comment: 28 pages, 20 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.10171 Zobrazit plný text záznamu View this record from Arxiv