TY - JOUR
T1 - Bifurcation of plane-to-plane map-germs of corank 2
AU - Yoshida, Toshiki
AU - Kabata, Yutaro
AU - Ohmoto, Toru
N1 - Funding Information:
This article is part of master-course theses of the first and second authors in Hokkaido university [9,22]. The authors thank Kentaro Saji for his interests, Farid Tari for making our attention to Janet West''s thesis and the referee for comments suggesting to improve the first draft. This work is partly supported by the JSPS grant no. 23654028.
Publisher Copyright:
© 2014. Published by Oxford University Press. All rights reserved.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - We describe the bifurcation diagrams of plane-to-plane map-germs of corank 2 up to Aecodimension 4, and draw some new pictures. Two applications are presented: First, we study the affine differential geometry of crosscaps in 3-space by means of analyzing singularities of projections of the singular surface to the plane. Secondly, we give some new examples of generic two-dimensional bifurcations of D4+-type planar caustics.
AB - We describe the bifurcation diagrams of plane-to-plane map-germs of corank 2 up to Aecodimension 4, and draw some new pictures. Two applications are presented: First, we study the affine differential geometry of crosscaps in 3-space by means of analyzing singularities of projections of the singular surface to the plane. Secondly, we give some new examples of generic two-dimensional bifurcations of D4+-type planar caustics.
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U2 - 10.1093/qmath/hau013
DO - 10.1093/qmath/hau013
M3 - Article
AN - SCOPUS:84954139642
SN - 0033-5606
VL - 66
SP - 369
EP - 391
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1
ER -