Growth of periodic orbits and generalized diagonals for typical triangle billiards

TL;DR

This paper provides an explicit sub-exponential estimate for the growth rate of periodic orbits and generalized diagonals in typical triangle billiards, advancing understanding of their dynamical complexity.

Contribution

It introduces a new explicit sub-exponential bound on the growth rate of orbits and diagonals in typical triangle billiards, which was previously unknown.

Findings

Established a sub-exponential growth estimate for periodic orbits.

Provided bounds on the number of generalized diagonals.

Enhanced understanding of dynamical complexity in billiard systems.

Abstract

We give an explicit sub-exponential estimate on the growth rate of periodic orbits and generalized diagonals for typical triangle billiards.