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首页> 外文会议>Third Meeting on Celestical Mechanics - CELMEC III Jun 18-22, 2001 Rome, Italy >STABLE CHAOS IN MEAN MOTION RESONANCES
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STABLE CHAOS IN MEAN MOTION RESONANCES

机译：平均运动共振中的稳定混沌

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摘要

One of the most interesting, newly discovered, phenomena in solar system dynamics is a type of asteroidal motion commonly referred to as stable chaos. An asteroid on stable chaotic motion (ASC) follows a strongly chaotic trajectory (as indicated by its short Lyapunov time, T_L = 1/λ, wheie λ is the Maximal Lyapunov Characteristic Number, LCN) and yet its orbital elements remain almost constant for thousands of Lyapunov times. The first example of an ASC, asteroid (522) Helga, was discovered by Milani & Nobili (1992) in the 12/7 orbital resonance with Jupiter. Since then, many more ASCs have been identified (e.g. see Milani et al., 1997; Sidlichovsky, 1999), in various orbital resonances with Jupiter. Therefore stable chaos seems to be a relatively common phenomenon in the solar system, usually associated with an orbital resonance with Jupiter. Since the discovery of this new phenomenon, many attempts were made in order to interpret the apparently controversial properties of chaotic motion, on the one hand, and stable orbital elements on the other. The first one was made by Milani & Nobili, who proposed that stable chaos is due to a secular protection mechanism, not related to the chaos-generating orbital resonance. Other interpretations of this phenomenon proposed since then include the use of diffusive transport (Murison et al., 1994, Murray & Holman, 1997) and the constructive superposition of critical terms in the disturbing function (Lemaitre, 1997). However all the above interpretations have some weak points. Varvoglis & Anastasiadis (1996), in trying to put the problem on a firm basis, stressed the fact that the LCN is related to the local properties of a dynamical system, while transport is related to both local and global (the latter related to the overall structure of phase space). As stated in the conclusions of this paper, "... the stable chaotic behavior of asteroids ... originates, most probably, from the presence of consecutive layers of quasi-barriers in certain regions of phase space, where transport is governed by Levy flights rather than random walks".
机译：太阳系动力学中最有趣的，新近发现的现象之一是一种小行星运动，通常称为稳定混沌。处于稳定混沌运动（ASC）的小行星遵循强烈的混沌轨迹（如其短的李雅普诺夫时间T_L = 1 /λ所示，其中λ是最大李雅普诺夫特征数LCN），但其轨道元素几千年来几乎保持不变利亚普诺夫时代。 ASC的第一个例子是小行星（522）Helga，由Milani＆Nobili（1992）在与木星的12/7轨道共振中发现。从那时起，在与木星的各种轨道共振中，已经发现了更多的ASC（例如，见Milani等，1997； Sidlichovsky，1999）。因此，稳定的混乱似乎是太阳系中相对普遍的现象，通常与木星的轨道共振有关。自从发现这种新现象以来，人们进行了许多尝试，以便一方面解释混沌运动的明显有争议的特性，另一方面又解释稳定的轨道元素。第一个是由Milani＆Nobili提出的，他提出稳定的混沌是由于世俗的保护机制引起的，与世俗的轨道共振无关。此后提出的对该现象的其他解释包括使用扩散运输（Murison等，1994； Murray＆Holman，1997）和扰动函数中关键项的构造性叠加（Lemaitre，1997）。但是，以上所有解释都有一些弱点。 Varvoglis＆Anastasiadis（1996）在试图将问题牢牢地放在基础上时，强调了以下事实：LCN与动力系统的局部特性有关，而运输与局部和全球性相关（后者与动力系统相关）。相空间的整体结构）。如本文结论所述：“……小行星的稳定混沌行为……最有可能是由于在某些相空间区域中存在连续的准屏障层，在这些区域中，运移是由征费控制的。而不是随机行走”。

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