标题： 平面热带奇点：三重性和凸性 显示英文标题

标题： Planar tropical caustics: trivalency and convexity

摘要： 平面上凸域的热带奇点是一条在该域内与之规范相关的热带解析曲线。 在本说明中，我们给出一种图形证明，用于对其中间顶点进行分类，这尤其表明这些顶点总是三价的。 除此之外，我们解释了各种已知的热带奇点的例子是如何构造的，并讨论了放松域的凸性条件的可能性。 显示英文摘要

摘要： Tropical caustic of a convex domain on the plane is a canonically associated tropical analytic curve inside the domain. In this note we give a graphical proof for the classification of its intermediate vertices, implying in particular that they are always trivalent. Apart from that we explain how various known examples of tropical caustics are constructed and discuss the possibility of relaxing the convexity condition for the domain.