论文标题
几何形状的定性理论与微分方程的整体叶子的定性理论之间的结构稳定范围相遇
An encounter in the realm of Structural Stability between a qualitative theory for geometric shapes and one for the integral foliations of differential equations
论文作者
论文摘要
这篇令人回味的文章着重于一些地标，这些地标使作者研究了$ \ Mathbb r^3 $的表面上的主要曲率配置，即它们的结构稳定性和通用属性。起点是与D. Struik书的相遇以及对Euler，Monge和Darboux在那儿发现的作品的参考。这些参考文献与1962年Peixoto在表面上的微分方程上的作品的串联是至关重要的第二步。 1982年至1983年，在这里叙述了融合到Gutiérrez和Sotomayor定理的情况。以上1982年至1983年的定理被指出为从1796年的蒙吉（Monge）著作中披露的思想界限之间的第一次相遇，1815年，杜宾（Dupin）和1896年的达伯克斯（Darboux），《庞加莱（Poincaré）成就，1881年，1881年，安德罗诺夫（Andronov -pontrjagin），1937年，1937年，1962年的1962年，奔跑于1881年的成就。在本文的最后一部分中提到。
This evocative essay focuses on some landmarks that led the author to the study of principal curvature configurations on surfaces in $\mathbb R^3$, their structural stability and generic properties. The starting point was an encounter with the book of D. Struik and the reading of the references to the works of Euler, Monge and Darboux found there. The concatenation of these references with the work of Peixoto, 1962, on differential equations on surfaces, was a crucial second step. The circumstances of the convergence toward the theorems of Gutiérrez and Sotomayor, 1982 - 1983, are recounted here. The above 1982 - 1983 theorems are pointed out as the first encounter between the line of thought disclosed from the works of Monge, 1796, Dupin, 1815, and Darboux, 1896, with that transpiring from the achievements of Poincaré, 1881, Andronov - Pontrjagin, 1937, and Peixoto, 1962. Some mathematical developments sprouting from the 1982 - 1983 works are mentioned on the final section of this essay.
