Webs and Singularities

Journal of Singularities
volume 9 (2014), 151-167

Received 3 January 2012. Received in revised form 22 December 2013.

DOI: 10.5427/jsing.2014.9l

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Abstract:

We investigate the singular web structure of first-order PDEs from the viewpoint of singularity theory. Most of the results given have already appeared in papers by others, as well as the author in various different terminologies. The new results are the construction of mini-versal webs from the deformation of isolated singularities, and their classification. We prove also the existence of the resonance curve for generic 3-webs with cuspidal singular locus. We introduce also Klein-Halphen webs with polyhedral symmetry and Fermat webs, and we investigate their properties.

Keywords:

Web, ODE, PDE, Hexagonal, Waves, Phase, Polyhedral group, Singularity, Resonance, Affine structure

Mathematical Subject Classification:

53A60, 14B05

Author(s) information:

Isao Nakai
Dept. Math., Faculty of Sci.
Ochanomizu Univ.
Bunkyo-ku, Ohtsuka 2-1-1, Tokyo, Japan
email: nakai.isao@ocha.ac.jp