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On the stability of bifurcation diagrams of vanishing flattening points. (English. Russian original) Zbl 1103.58019
Funct. Anal. Appl. 37, No. 3, 236-240 (2003); translation from Funkts. Anal. Prilozh. 37, No. 3, 88-94 (2003).
Summary: On a smooth surface in Euclidean 3-space, we consider vanishing curves whose projections on a given plane are small circles centered at the origin. The bifurcation diagram of a parameter-dependent surface is the set of parameters and radii of the circles corresponding to curves with degenerate flattening points. Solving a problem due to Arnold, we find a normal form of the first nontrivial example of a flattening bifurcation diagram, which contains one continuous invariant.

58K15 Topological properties of mappings on manifolds
58K25 Stability theory for manifolds
53A05 Surfaces in Euclidean and related spaces
37G10 Bifurcations of singular points in dynamical systems
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