-symmetric planar polynomial Hamiltonian systems of
degree 3 with nilpotent centers
-symmetric planar polynomial Hamiltonian systems of
degree 3 with nilpotent centers
Fabio Scalco Dias, Jaume Llibre, Claudia Valls
Abstract:
We provide the normal forms of all
-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