|
|
|
题名
|
作者
|
年代
|
出处
|
被引量
|
| 1 | The Stability of the Elliptic Equilibrium of Planar Quasi-periodic Hamiltonian Systems显示文摘In this paper, we study the planar Hamiltonian system = J (A(θ)x + ▽f(x, θ)), θ = ω, x ∈ R2 , θ∈ Td , where f is real analytic in x and θ, A(θ) is a 2 × 2 real analytic symmetric matrix, J = (1-1 ) and ω is a Diophantine vector. Under the assumption that the unperturbed system = JA(θ)x, θ = ω is reducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system. | Yun Chao WU Yi Qian WANG | 2012 | Acta Mathematica Sinica,English Series2012，28，4： | 2 |
| 2 | Boundedness in Asymmetric Quasi-periodic Oscillations显示文摘In the paper, by applying the method of main integration, we show the boundedness of the quasi-periodic second order differential equation x′′+ ax^+-bx^-+φ(x) = p(t), where a≠b are two positive constants and φ(s), p(t) are real analytic functions. Moreover, the p(t) is quasi-periodic coefficient, whose frequency vectors are Diophantine. The results we obtained also imply that, under some conditions,the quasi-periodic oscillator has the Lagrange stability. | Xing Xiu-mei Ma Jing Jiao Lei | 2017 | Communications in Mathematical Research2017，33，2： | 0 |
| 3 | 拟周期平面振子平衡点的稳定性显示文摘利用主积分方法,将周期系统平衡点的稳定性判据推广到拟周期情形,即证明拟周期二阶微分方程x″+h(t)x′+a(t)x2n+1+e(t,x)=0(n≥1)平衡点x=x′=0的稳定性,其中h(t),a(t),e(t,x)是拟周期系数,其频率向量满足Diophantine条件,且在x=x′=0附近,|e(t,x)|=O(x2n+2).结果表明,具有变号阻尼项拟周期振子的平衡点在一定条件下具有稳定性. | 邢秀梅 任秀芳 | 2015 | 吉林大学学报(理学版)2015，53，3： | 0 |
| 4 | 共振情形下拟周期Hamiltonian系统的线性化显示文摘受Rsmann的工作的启发,本文考虑实解析拟周期Hamiltonian系统{■=i(ρz+(f)/(z)(z,■,θ))■=ω,其中P≥0,z∈C,θ∈T^d且f=O_3(|z|).假设ω是Diophantine向量,且P与ω共振.本文证明如果系统是形式可线性化的,则它也是解析可线性化的.从而该系统的不动点是Lyapunov稳定的. | 吴云超 | 2012 | 数学进展2012，41，5： | 0 |
您所在的机构暂未开通此部分的功能，请联系管理员