Limits of the Formal Integrals of Motion

George Contopoulos, Athanasios C. Tzemos, Foivos Zanias

We consider a formal (approximate) integral of motion in Hamiltonians of the form $H=\frac{1}{2}(X^2+Y^2+{\omega }_1^2{x}^2+{\omega }_2^2{y}^2)+\epsilon (\eta x{y}^2+\alpha x^3+\beta x^{2}y+\gamma y^3)$ generalizing previous cases wi…