可积系统的结构稳定非退化奇异性

IF 1.7 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
E. A. Kudryavtseva, A. A. Oshemkov
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引用次数: 1

摘要

本文研究了由完全可积系统给出的拉格朗日振动的奇异性。证明了满足连通条件的非简并奇异光纤在系统的(足够小的)实解析可积扰动下是结构稳定的。换句话说,在任何这样的扰动之后,在这样的纤维的一个邻域中的纤维的拓扑结构被保留。作为例证,我们证明了Kovalevskaya顶的简单鞍-鞍奇点在实解析可积摄动下是结构稳定的,而在\(C^\infty\) -光滑可积摄动下不是结构稳定的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Structurally Stable Nondegenerate Singularities of Integrable Systems

In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a nondegenerate singular fiber satisfying the so-called connectedness condition is structurally stable under (small enough) real-analytic integrable perturbations of the system. In other words, the topology of the fibration in a neighborhood of such a fiber is preserved after any such perturbation. As an illustration, we show that a simple saddle-saddle singularity of the Kovalevskaya top is structurally stable under real-analytic integrable perturbations and not structurally stable under \(C^\infty\)-smooth integrable perturbations.

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来源期刊
Russian Journal of Mathematical Physics
Russian Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
14.30%
发文量
30
审稿时长
>12 weeks
期刊介绍: Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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