Boundedness of solutions for a class of impact oscillators with time-dependent polynomial potentials (Q380157)

By making use of action-angle variables and Moser's small twist theorem, the authors prove the boundedness of the solutions of a nonlinear impact oscillator with periodically time-dependent polynomial potential given by NEWLINE\[NEWLINE \ddot{x}+x^{2n+1}+\sum_{i=1}^{2n} p_i(t)x^i=0, NEWLINE\]NEWLINE with the impact condition NEWLINE\[NEWLINE x(t_0)=0\implies \dot{x}(t_0^+)=-\dot{x}(t_0^-), NEWLINE\]NEWLINE and the regularity assumption \(p_i\in C^5\).