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math.DS2024
On the Factor Complexity Associated with a Family of Multidimensional Continued Fraction Algorithms
Thomas Garrity, Otto Vaughn Osterman
We study the complexity of -adic sequences corresponding to a family of 216 multidimensional continued fractions maps, called Triangle Partition maps (TRIP maps), with an emphas…
math.DS2022
On Length Spectrum Rigidity of Dispersing Billiard Systems
Otto Vaughn Osterman
We consider the class of dispersing billiard systems in the plane formed by removing three convex analytic scatterers satisfying the non-eclipse condition. The collision map in thi…
math.DS2019
On the Density of Dispersing Billiard Systems with Singular Periodic Orbits
Otto Vaughn Osterman
Dynamical billiards, or the behavior of a particle traveling in a planar region undergoing elastic collisions with the boundary, has been extensively studied and is used to mod…