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math.DS2025
Chaotic Boltzmann's Billiard Systems at positive energy
Irene De Blasi, Airi Takeuchi, Susanna Terracini
This paper deals with the so-called Boltzmann billiard, that is, a billiard subjected to a central force of the type , and being positive constants, and wi…
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
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…