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math.DS2013★ 2 cited
Billiard dynamics of bouncing dumbbell
Y. Baryshnikov, V. Blumen, K. Kim +1
A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions w…
math.DS2011
Three-Period Orbits in Billiards on the Surfaces of Constant Curvature
Victoria Blumen, Ki Yeun Kim, Joe Nance +1
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is fou…