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

Volume 12, Issue 11, pp 711--719 http://dx.doi.org/10.22436/jnsa.012.11.02

Publication Date: June 15, 2019 Submission Date: June 08, 2018 Revision Date: May 08, 2019 Accteptance Date: May 28, 2019

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Authors

Fuzhong Cong - Fundamental Department, Aviation University of Air Force Changchun, 130022, People's Republic of China. Tianchu Hao - Fundamental Department, Aviation University of Air Force Changchun, 130022, People's Republic of China. Xue Feng - Fundamental Department, Aviation University of Air Force Changchun, 130022, People's Republic of China.

Abstract

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, \(\bf 21\) (2016), 67--80] to time-dependent system and gave a connection between KAM theorem and effective stability.

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Keywords

• Quasi-effective stability
• non-degeneracy
• time-dependent system

MSC

•  37J25
•  37J40

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