原始 发表于 2025-3-25 07:22:59

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cochlea 发表于 2025-3-25 10:32:51

Singularities of the Stability Boundary and the Principle of the Fragility of Good Things,Let us consider an equilibrium state of a system depending on several parameters and let us assume that (in some domain of variation of the parameters) this equilibrium state does not bifurcate.

Cuisine 发表于 2025-3-25 13:37:46

Singularities of the Boundary of Attainability,A . in phase space is defined as follows: at every point of the space we have not just one velocity vector (as in the usual evolutionary system), but a whole set of vectors called the ..

Obvious 发表于 2025-3-25 19:25:54

Smooth Surfaces and Their Projections,A smooth curve on the plane can have a tangent which touches it tangentially at any number of points, but this is not true for generic curves. By a small perturbation of the curve one can always achieve that no straight line will be tangential at more than two points.

不如乐死去 发表于 2025-3-25 21:55:00

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彻底检查 发表于 2025-3-26 03:08:02

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母猪 发表于 2025-3-26 08:10:32

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neutrophils 发表于 2025-3-26 11:21:46

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空洞 发表于 2025-3-26 12:53:03

https://doi.org/10.1007/978-3-031-47444-6 the obstacle consists of straight-line segments and segments of geodesics (curves of minimal length) on the surface of the obstacle. The geometry of the shortest paths is greatly affected by the various bendings of the obstacle surface.

Glaci冰 发表于 2025-3-26 19:26:02

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查看完整版本: Titlebook: Catastrophe Theory; Vladimir I. Arnold Book 1992Latest edition Springer-Verlag Berlin Heidelberg 1992 Bifurcations.Catastrophe Theory.Kata