KAM theorem for reversible mapping of low smoothness with application

2019/10/18 by Jing Li, Li, Jing, Jiangang Qi +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1910.08214

openalex publication_date 2019/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assume the mapping A:\ x₁=x+ω+y+f(x,y), y₁=y+g(x,y), . (x, y)∈ \mathbbT^d× B(r₀) is reversible with respect to G: (x, y)↦ (-x, y), and | f | _C^ℓ(\mathbbT^d× B(r₀))≤ ε₀, | g |_C^ℓ+d(\mathbbT^d× B(r₀))≤ ε₀, where B(r₀):=\|y|≤ r₀: y∈\mathbb R^d\, ℓ=2d+1+μ with 00 is small enough and ω is Diophantine, the map A possesses an invariantS torus with rotational frequency ω. As an application of the obtained theorem, the Lagrange stability is proved for a class of reversible Duffing equation with finite smooth perturbation.

Related

• Lagrange Stability for Reversible Duffing Equations with Quasi-Periodic Coefficients
• KAM below \mathbf Cⁿ
• Invariant curves of low smooth quasi-periodic reversible mappings
• KAM theorem with large twist and finite smooth large perturbation
• Asymptotic trajectories of KAM torus