一个哈密顿系统正则动量的软模振荡

本文进一步研究了以前提出的哈密顿系统,说明非线性振子的实振幅具有的极限圈运动,由于另一类模式耦合扰动,引起振子的线性频率重新激发,而失稳到二维环。据此,分析了有关的实验及理论研究,推断流体力学矩方程之间的耦合,可能在显示Ruelle-Takens途径上起了关键作用,同时猜想向湍流转变的图象是轨迹被吸引在两个二维环上不断调节的运动。

SOFT-MODE OSCILLATIONS OF CANONICAL MOMENTA IN A HAMILTONIAN SYSTEM

The Hamiltonian proposed previously is further studied. It is shown that the limit cycles of the real amplitudes of the interacting nonlinear oscillators may lose stabilities and become 2-tori owing to the re-excitation of the linear frequencies of the oscillators,which is attributed to the coupling perturbation of another kind of modes.From this as well as other authors results it is conjectured that the coupling between the moment equations of hydrodynamics may play a critical role in Ruelle-Takens route, and the picture of transition to turbulence is conceived as an adjusted motion attracted on two 2-tori.