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首页> 外文会议>Third Meeting on Celestical Mechanics - CELMEC III Jun 18-22, 2001 Rome, Italy >STUDY OF THE HAMILTONIAN NORMAL FORM NEAR A RESONANT PERIODIC ORBIT
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STUDY OF THE HAMILTONIAN NORMAL FORM NEAR A RESONANT PERIODIC ORBIT

机译：共振周期轨道附近的哈密顿正态形式的研究

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To be more precise, we suppose that, for σ < 0, those nontrivial characteristic multipliers of M_σ lie on the unit circle, they approach pairwise as σ goes to σ = 0, for this value they collide and separate towards the complex plane when σ > 0. In addition, it is assumed that the collision is irrational. This means that the critical (i. e., the one corresponding to σ = 0) periodic orbit, has two characteristic exponents with opposite signs and these are not commensurable with 2π. The evolution of the characteristic multipliers along the family is plotted in figure 1. The instabilization process just described is known in the literature as the transition from stability to complex instability, and far from being a rare or strange phenomenon, there are plenty examples from several fields ranging from galactic dynamics to particle accelerators (see for example).
机译：更准确地说，我们假设，对于σ<0，M_σ的那些非平凡特征乘数位于单位圆上，当σ到达σ= 0时，它们成对逼近；对于该值，当σ时，它们碰撞并向复平面分离>0。此外，假定碰撞是不合理的。这意味着临界（即，对应于σ＝ 0的那个）周期性轨道具有两个具有相反符号的特征指数，并且这些特征指数与2π不能相称。图1绘出了特征乘数沿该族的演变。文献中将刚刚描述的不稳定过程称为从稳定到复杂不稳定的过渡，并且它不是稀有或奇怪的现象，有许多例子从银河系动力学到粒子加速器的各个领域（例如参见）。

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