49 citations · 143 across the 23 of their papers we have counts for
23 papers
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…
Darboux inversions of the Kepler problem
Alain Albouy, Lei Zhao
While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with t…
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…
Projective Dynamics and an Integrable Boltzmann Billiard Model
Lei Zhao
The aim of this note is to explain the integrability of an integrable Boltzmann billiard model, previously established by Gallavotti and Jauslin in arXiv:2008.01955, alternatively…
Generalized periodic orbits in some restricted three-body problems
Rafael Ortega, Lei Zhao
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this s…