On the envelope of 1-parameter families of curves tangent to a semicubic cusp (Q1854698)

Let \(\gamma\) be a real plane curve, with a semicubical cusp point \(O\). Consider a one-parameter family of curves tangent to \(\gamma\) such that their radius of curvature at the tangency point vanishes as the tangency point approaches \(O\). The author shows that, generically, the closure of the envelope of this family has two semicubic cusps at \(O\), tangent to the same straight line, one of which is \(\gamma\). Nongeneric and dual cases are also studied.