Geodesic
Geometry of bifurcation diagrams
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 22 (1983), pp. 94-129
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The geometry of a bifurcation diagram in the base of a versal deformation of a singularity is studied for single singularities on a manifold with boundary. In particular, vector fields and groups of diffeomorphisms are studied which are defined in a neighborhood of a bifurcation diagram as are stratification of a bifurcation diagram and decomposition of singularities. 
@article{INTD_1983_22_a2,
     author = {O. V. Lyashko},
     title = {Geometry of bifurcation diagrams},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {94--129},
     year = {1983},
     volume = {22},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1983_22_a2/}
}
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O. V. Lyashko. Geometry of bifurcation diagrams. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 22 (1983), pp. 94-129. http://geodesic.mathdoc.fr/item/INTD_1983_22_a2/