4 papers
The kei word metric on the transvection group and its unit ball
Urs Frauenfelder, Lei Zhao
We define a bi-invariant word metric on a group using keis. We discuss whether such a word metric is trivial or non-trivial in various examples coming from group theory, dynamical…
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…
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,…
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…