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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.

MSC:
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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