Quasi-effective stability for nearly integrable Hamiltonian systems

Abstract

This paper concerns with the stability of the orbits for nearly integrable Hamiltonian systems. Based on Nekehoroshev's original works in [14], we present the definition of quasi-effective stability and prove a theorem on quasi-effective stability under the Rüssmann's non-degeneracy. Our result gives a relation between KAM theorem and effective stability. A rapidly converging iteration procedure with two parameters is designed.2010 Mathematics Subject Classification. 37J25, 37J40, 70H08.

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

“…Under the Rüssmann's non-degeneracy, we also can obtain the same conclusion as in Theorem 1.2. This need to apply the technique in [3,4].…”

“…The definition of quasi-effective stability is proposed in the literatures [3,4]. This concept is a generalization of effective stability developed by Nekhoroshev [8].…”