Generic deformations of Lagrangian and Legendrian maps

TL;DRAbstract

a. Investigating ocean and atmosphere flows Nye and Thorndike [2] have studied typical bifurcations of three dimensional vector fields depending on time. One can describe such a field as a one-parameter family of maps from R to R or as a map from R×R = R to R. To study them the authors of [2] consider sections of stable maps from R to R. There is one family in their list of typical sections for which the set of critical values for an isolated value of the parameter is equal to the caustic of a Lagrangian D4 map. This leads to another problem: To study properties of Lagrangian and Legendrian maps included in generic families of maps with a suitable number of parameters. In this way V -versal deformations of Lagrangian Dk and Legendrian Ak maps are considered below.

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