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arXiv · 2606.08358

Explicit Families and Distribution of Triangular Billiards of Weakly Exponential Growth

Irina Mamsurova
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Abstract

Recently, it has been shown that the combinatorial complexity function $N_c(n)$ of a typical triangular billiard has weakly exponential growth, i.e., for almost any triangle and any $\varepsilon>0$ there is a constant $C$ such that $N_c(n)<Ce^{n^\varepsilon}$. We give the first example, an infinite family of explicitly described triangles with weakly exponential complexity growth. The simplest example in this family is a right triangle with integer side lengths. Moreover, we find one-parameter families of triangular tables with weakly exponential growth for generic parameters.

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Irina Mamsurova. 2026-06-06. Explicit Families and Distribution of Triangular Billiards of Weakly Exponential Growth. https://arxiv.org/abs/2606.08358

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