New family of cubic Hamiltonian centers
Consider the polynomial Hamiltonian system \[ \begin{aligned} {dx\over dt} &= -y-(bx+ 2cy)(x+ax^2+ bxy+ cy^2),\\ {dy\over dt} &= (1+ 2ax+ by)(x+ax^2+ bxy+ cy^2)\end{aligned}\tag{\(*\)} \] with the Hamiltonian \[ H={1\over 2} ((x+ ax^2+ bxy+ cy^2)^2+ y^2) \] under the assumption \(a^2+ b^2+ c^2\neq 0\). The authors characterize the phase portrait of \((*)\) in the Poincaré disc. They prove the existence of 11 classes of phase portraits which topologically not equivalent.
scientific article; zbMATH DE number 6835193
scientific article