Abstract
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.
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Uribe-Vargas, R. On the Stability of Bifurcation Diagrams of Vanishing Flattening Points. Functional Analysis and Its Applications 37, 236–240 (2003). https://doi.org/10.1023/A:1026096919765
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DOI: https://doi.org/10.1023/A:1026096919765