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math.DS2023
Boltzmann's Billiard Systems: Computation of the Billiard Mapping and Some Numerical Results
Michael Plum, Airi Takeuchi, Lei Zhao
L. Boltzmann proposed a billiard model with a planar central force problem reflected against a line not passing through the center. He asserted that such a system is ergodic, which…
math.DS2023
Kustaanheimo-Stiefel Transformation, Birkhoff-Waldvogel Transformation and Integrable Mechanical Billiards
Airi Takeuchi, Lei Zhao
The three-dimensional Kepler problem is related to the four-dimensional isotropic harmonic oscillators by the Kustaanheimo-Stiefel Transformations. In the first part of this paper,…
math.DS2023
Concave Toric Domains in Stark-type Mechanical Systems
Airi Takeuchi, Lei Zhao
It has been shown in [Frauenfelder, 2023] that the bounded component of the energy surface of the planer Stark problem after the Levi-Civita transformation are concave toric domain…