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math.DS2023
Star-shaped trajectories of certain billiards around a triangle
Takeo Noda, Shin-ichi Yasutomi, Masamichi Yoshida
We explore the triangle outer billiards map in points at infinity in the hyperbolic plane, focusing on the rotation number. Building on Dogru and Tabachnikov's work, which establis…
math.DS2021
Billiards in a circle with trajectories circumscribing a triangle
Takeo Noda, Shin-ichi Yasutomi
Dogru and Tabachnikov in 2003 explored the polygonal outer billiard map in the hyperbolic plane and introduced a class of convex polygons called 'large'. They particularly sought c…
math.DS2020
Ergodicity for -adic continued fraction algorithms
Hui Rao, Shin-ichi Yasutomi
Following Schweiger's generalization of multidimensional continued fraction algorithms, we consider a very large family of -adic multidimensional continued fraction algorithms,…