33 citations · 97 across the 16 of their papers we have counts for
18 papers
Horns in Billiards
David de Frutos Ostrander, Boris Hasselblatt, Mark Levi
We show that, like cusps, horns in billiards expel every trajectory after finitely many collisions. We further produce an adiabatic invariant.
Arnold Tongues in Area-Preserving Maps
Jing Zhou, Mark Levi
In the early 60's J. B. Keller and D. Levy discovered a fundamental property: the instability tongues in Mathieu-type equations lose sharpness with the addition of higher-frequency…
Open problems on billiards and geometric optics
M. Bialy, C. Fierobe, A. Glutsyuk +3
This is a collection of open problems from workshop "Differential Geometry, Billiards, and Geometric Optics" at CIRM on October 4-8, 2021.
Spectral asymptotics and Lamé spectrum for coupled particles in periodic potentials
Ki Yeun Kim, Mark Levi, Jing Zhou
We make two observations on the motion of coupled particles in a periodic potential. Coupled pendula, or the space-discretized sine-Gordon equation is an example of this problem. L…
Hill's equation, tire tracks and rolling cones
Gil Bor, Mark Levi
Louis Poinsot has shown in 1854 that the motion of a rigid body, with one of its points fixed, can be described as the rolling without slipping of one cone, the 'body cone', along…
The ponderomotive Lorentz force
Graham Cox, Mark Levi
This paper describes a curious phenomenon: a particle in a rapidly varying potential is subject to an effective magnetic-like force. This force is in addition to the well-known pon…