Destruction of Lagrangian torus for positive definite Hamiltonian systems

2012/11/27 by Chong-Qing Cheng, Lin Wang, Cheng, Chong-Qing +1 · 2 citations
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1211.6480

openalex publication_date 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an integrable Hamiltonian H₀=1/2∑_i=1^dy_i² (d≥ 2), we show that any Lagrangian torus with a given unique rotation vector can be destructed by arbitrarily C^2d-δ-small perturbations. In contrast with it, it has been shown that KAM torus with constant type frequency persists under C^2d+δ-small perturbations.

Cited by

• Herman's converse KAM mechanism revisited
• An infinite-dimensional Kolmogorov theorem and the construction of almost periodic breathers

Related

• Quantitative Destruction and Persistence of Lagrangian Torus in Hamiltonian Systems
• Converse KAM theory revisited
• A note on the KAM theorem for partially integrable Hamiltonian systems
• KAM Theorems for Multi-scale Torus
• KAM theorem with large perturbation and application to network of Duffing oscillators