Numerical Experiments on the Tricorn

This note gives numerical experiments and an intuitive explanation of the non-pathwise connectivity of the tricorn, the connectedness locus of the family of antiquadratic polynomials

Stretching Rays at Critically Prefixed Real Cubic Polynomials

In this note, the dynamics of real cubic polynomials is considered. Especially, in the parameter space, landing of stretching rays at critically prefixed polynomials is investigated. It turns out that an interval worth of stretching rays land at such points

2ジゲンホゾンソク ニ タイスル ショウゲキハ ノ セイセイ

The initial value problem for an equation of scalar conservation law in two-space dimensions is considered. By the method of characteristics, the solution of this problem is concretely constructed. Especially, under some generic assumptions, formation of shocks is exactly described. lt is easily seen from our results where shocks occur. In these processes, singularity theory plays an essential role