Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 82, pp. 1-29.

Title: Z2-symmetric planar polynomial Hamiltonian systems of
       degree 3 with nilpotent centers

Authors: Fabio Scalco Dias (Univ. Federal de Itajuba, MG, Brazil)
         Jaume Llibre  (Univ. Autonoma de Barcelona, Spain)
         Claudia Valls (Univ. de Lisboa, Portugal)

Abstract:
 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.