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Non-periodic not everywhere dense trajectories in triangular billiards (2406.17734v1)
Published 25 Jun 2024 in math.DS
Abstract: Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a one-parameter family of isosceles triangles exhibiting non-periodic trajectories that are not everywhere dense. This provides, by elementary means, a definitive negative answer to a long-standing open question on the density of non-periodic trajectories in triangular billiards.