Examples of nearly integrable systems on ${\mathbb{A}}^3$ with asymptotically dense projected orbits

Jean-Pierre Marco, Lara Sabbagh

Given an integer $\kappa \ge 2$, we introduce a class of nearly integrable systems on ${\mathbb{A}}^3$, of the form $$H_n(\theta ,r)=\frac{1}{2}\Vert r{\Vert }^2+\frac{1}{n}U({\theta }_2,{\theta }_3)+f_n(\theta ,r)$$…