Quasi-effective stability for time-dependent nearly integrable Hamiltonian systems

This paper deals with the stability of the orbits for time-dependent nearly integrable Hamiltonian systems. Under the classical non-degeneracy in KAM theory we prove that the considered system possesses quasi-effective stability. Our result generalized the works in [F. Z. Cong, J. L. Hong, H. T. Li, Dyn. Syst. Ser. B, 21 (2016), 67–80] to time-dependent system and gave a connection between KAM theorem and effective stability.