In this paper we completely characterize trivial polynomial Hamiltonian isochronous centers of degrees 5 and 7. Precisely, we provide simple formulas, up to linear change of coordinates, for the Hamiltonians of the form H = (f21 + f22)/2, where f = (f1, f2) : R2 → R2 is a polynomial map with det Df = 1, f(0, 0) = (0; 0) and the degree of f is 3 or 4.
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 1 Oct 2016|
- Isochronous centers
- Jacobian conjecture
- Polynomial Hamiltonian systems