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

原始

cochlea

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

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

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.

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母猪

neutrophils

空洞

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.

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