耗散诱导失稳的悖论，或谁打开了惠特尼伞？
Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?
AI总结：
本文回顾了Bottema在1956年利用惠特尼伞奇点对Ziegler悖论（小耗散导致保守或非保守系统失稳）的首次完整解释，并讨论了后续发展，包括矩阵结构稳定性、Krein碰撞、Hamilton-Hopf分岔及相关分岔。
摘要：
小耗散导致保守或非保守系统失稳的悖论，即Ziegler悖论（1952），激发了人们对可逆系统和哈密顿系统对耗散扰动敏感性的日益增长的兴趣。自过去十年以来，人们普遍认为耗散诱导的不稳定性与稳定性边界上出现的奇点密切相关。鲜为人知的是，利用惠特尼伞奇点对Ziegler悖论的首次完整解释可追溯到1956年。我们重新审视了Oene Bottema这一被不公正遗忘的开创性成果，它比后来的发现领先了大约半个世纪。我们讨论了这一时期耗散诱导不稳定性扰动分析及其应用的后续发展，涉及矩阵的结构稳定性、Krein碰撞、Hamilton-Hopf分岔及相关分岔。
英文摘要：
The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.
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