The quasi-periodic stability condition (the KAM theorem) for partially-integrable systems

2003/01/08 by G. Sardanashvily, Sardanashvily, G.
Mathematics · Physics and Astronomy · #37J40 #70H08 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum chaos and dynamical systems #math-ph #math.DS #math.MP #msc:37J40 #msc:70H08

paper · pdf · doi:10.48550/arxiv.math/0301068

4 pages

arxiv created 2003/01/08 · openalex publication_date 2003/01/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Written with respect to an appropriate Poisson structure, a partially integrable Hamiltonian system is viewed as a completely integrable system with parameters. Then, the theorem on quasi-periodic stability in Ref. [1] (the KAM theorem) can be applied to this system.

Related

• A note on the KAM theorem for partially integrable Hamiltonian systems
• Resonant equilibrium configurations in quasi-periodic media: KAM theory
• Some stability properties of Hamiltonian Poisson integrators
• Quasi-periodic motions on symplectic tori
• KAM estimates for the dissipative standard map