Simultaneity of centres in ℤ q -equivariant systems

Jaume Giné; Jaume Llibre; Claudia Valls

doi:10.1098/rspa.2017.0811

Simultaneity of centres in ℤ _q -equivariant systems

Proc Math Phys Eng Sci. 2018 May;474(2213):20170811. doi: 10.1098/rspa.2017.0811. Epub 2018 May 9.

Authors

Jaume Giné¹, Jaume Llibre², Claudia Valls³

Affiliations

¹ Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain.
² Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain.
³ Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal.

Abstract

We study the simultaneous existence of centres for two families of planar $Z_{q}$ -equivariant systems. First, we give a short review about $Z_{q}$ -equivariant systems. Next, we present the necessary and sufficient conditions for the simultaneous existence of centres for a $Z_{2}$ -equivariant cubic system and for a $Z_{2}$ -equivariant quintic system.

Keywords: centre–focus problem; equivariant system; first integrals; simultaneity of centres.