200 research outputs found
Hyperbolic outer billiards : a first example
We present the first example of a hyperbolic outer billiard. More precisely
we construct a one parameter family of examples which in some sense correspond
to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit
Rotating Leaks in the Stadium Billiard
The open stadium billiard has a survival probability, , that depends on
the rate of escape of particles through the leak. It is known that the decay of
is exponential early in time while for long times the decay follows a
power law. In this work we investigate an open stadium billiard in which the
leak is free to rotate around the boundary of the stadium at a constant
velocity, . It is found that is very sensitive to . For
certain values is purely exponential while for other values the
power law behaviour at long times persists. We identify three ranges of
values corresponding to three different responses of . It is
shown that these variations in are due to the interaction of the moving
leak with Marginally Unstable Periodic Orbits (MUPOs)
The maximum number of cycles in a triangular-grid billiards system with a given perimeter
Given a (simple) grid polygon in a grid of equilateral triangles, Defant
and Jiradilok considered a billiards system where beams of light bounce around
inside of . We study the relationship between the perimeter
of and the number of different trajectories
that the billiards system has. Resolving a conjecture
of Defant and Jiradilok, we prove the sharp inequality and characterize the equality cases.Comment: 21 pages, 21 figure
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