形式运动积分的极限
混沌动力学
2026-01-22 v1
摘要
我们考虑形如 H = 1 2 ( X 2 + Y 2 + ω 1 2 x 2 + ω 2 2 y 2 ) + ϵ ( η x y 2 + α x 3 + β x 2 y + γ y 3 ) H=\frac{1}{2}(X^2+Y^2+\omega_1^2x^2+\omega_2^2y^2)+\epsilon(\eta xy^2+\alpha x^3+\beta x^2y+\gamma y^3) H = 2 1 ( X 2 + Y 2 + ω 1 2 x 2 + ω 2 2 y 2 ) + ϵ ( η x y 2 + α x 3 + β x 2 y + γ y 3 ) β = γ = 0 \beta=\gamma=0 β = γ = 0 ω 1 / ω 2 \omega_1/\omega_2 ω 1 / ω 2 ω 1 / ω 2 = 4 / 1 , 5 / 1 , 3 / 2 , 4 / 3 , 3 / 1 \omega_1/\omega_2=4/1, 5/1, 3/2, 4/3, 3/1 ω 1 / ω 2 = 4/1 , 5/1 , 3/2 , 4/3 , 3/1 2 / 1 2/1 2/1 ω 1 / ω 2 = 2 / 1 \omega_1/\omega_2=2/1 ω 1 / ω 2 = 2/1 1 / 1 1/1 1/1 β = γ = 0 \beta=\gamma=0 β = γ = 0 β γ ≠ 0 \beta\gamma\neq0 β γ = 0 ω 1 / ω 2 = 1 / 1 \omega_1/\omega_2=1/1 ω 1 / ω 2 = 1/1 β = γ = 0 \beta=\gamma=0 β = γ = 0 η α ≠ 0 \eta\alpha\neq0 η α = 0 η = α = 0 \eta=\alpha=0 η = α = 0 β γ ≠ 0 \beta\gamma\neq 0 β γ = 0 η α β γ ≠ 0 \eta\alpha\beta\gamma\neq 0 η α β γ = 0 ω 1 / ω 2 = 5 2 / 7 = 1.010 … \omega_1/\omega_2=5\sqrt{2}/7=1.010\dots ω 1 / ω 2 = 5 2 /7 = 1.010 …
引用
@article{arxiv.2601.14899,
title = {Limits of the Formal Integrals of Motion},
author = {George Contopoulos and Athanasios C. Tzemos and Foivos Zanias},
journal= {arXiv preprint arXiv:2601.14899},
year = {2026}
}
备注
10 Figures