2 citations · 2 across the 6 of their papers we have counts for
7 papers
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…
Integrable Mechanical Billiards in Higher Dimensional Space Forms
Airi Takeuchi, Lei Zhao
In this article, we consider mechanical billiard systems defined with Lagrange's integrable extension of Euler's two-center problems in the Euclidean space, on the sphere, and in t…
Projective Integrable Mechanical Billiards
Airi Takeuchi, Lei Zhao
In this paper, we use the projective dynamical approach to integrable mechanical billiards as in [Zhao, 2021] to establish the integrability of natural mechanical billiards with th…
On the magic square C*-algebra of size 4
Takeshi Katsura, Masahito Ogawa, Airi Takeuchi
In this paper, we investigate the structure of the magic square C*-algebra of size 4. We show that a certain twisted crossed product of is isomorphic to the homogeneo…
Conformal Transformations and Integrable Mechanical Billiards
Airi Takeuchi, Lei Zhao
In this article we explain that several integrable mechanical billiards in the plane are connected via conformal transformations. We first remark that the free billiard in the plan…