Geodesic
On the Stability of Bifurcation Diagrams of Vanishing Flattening Points
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 3, pp. 88-94

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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 bifurcations 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.
Keywords: flattening point, bifurcation diagram, singularity of a family of mappings. 
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     title = {On the {Stability} of {Bifurcation} {Diagrams} of {Vanishing} {Flattening} {Points}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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R. Uribe-Vargas. On the Stability of Bifurcation Diagrams of Vanishing Flattening Points. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 3, pp. 88-94. http://geodesic.mathdoc.fr/item/FAA_2003_37_3_a9/