Uribe-Vargas, R. 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. Cited in 3 Documents 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 Keywords:flattening point; bifurcation diagram; singularity of a family of mappings PDF BibTeX XML Cite \textit{R. Uribe-Vargas}, Funct. Anal. Appl. 37, No. 3, 236--240 (2003; Zbl 1103.58019); translation from Funkts. Anal. Prilozh. 37, No. 3, 88--94 (2003) Full Text: DOI