Electron. J. Differential Equations, Vol. 2019 (2019), No. 82, pp. 1-29.

$\mathbb{Z}_2$-symmetric planar polynomial Hamiltonian systems of degree 3 with nilpotent centers

Fabio Scalco Dias, Jaume Llibre, Claudia Valls

We provide the normal forms of all $\mathbb{Z}_2$-symmetric planar polynomial Hamiltonian systems of degree 3 having a nilpotent center at the origin. Furthermore, we complete the classification of the global phase portraits in the Poincare disk of the above systems initiated by Dias, Llibre and Valls [9].

Submitted October 16, 2018. Published June 14, 2019.
Math Subject Classifications: 34C05, 34C07, 34C08.
Key Words: Polynomial Hamiltonian systems; nilpotent center; phase portrait; Poincare compactification; Z2-symmetric.

Show me the PDF file (618 KB), TEX file for this article.

Fabio Scalco Dias
Instituto de Matemática e Computação
Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho
CEP 37.500--903, Itajubá, MG, Brazil
email: scalco@unifei.edu.br
Jaume Llibre
Departament de Matemàtiques
Universitat Aut&ogfrave;noma de Barcelona
08193 Bellaterra, Barcelona, Spain
email: jllibre@mat.uab.cat
  Claudia Valls
Departamento de Matemática
Instituto Superior Técnico
Universidade de Lisboa
1049-001 Lisboa, Portugal
email: cvalls@math.ist.utl.pt

Return to the EJDE web page