Fractal analysis on a closed classical hard-wall billiard using a simplified box-counting algorithm

Details Fractal analysis on a closed classical hard-wall billiard using a simplified box-counting algorithm Fractal analysis on a closed classical hard-wall billiard using a simplified box-counting algorithm

2002-08-27

arxiv.org/abs/nlin/0208037v1

Chaos, Solitons & Fractals, 18, pp. 843-847 (2003)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures

Scientific paper

10.1016/S0960-0779(03)00036-5

We perform fractal analysis on a closed classical hard-wall billiard, the circular billiard with a straight cut, assuming there are two openings on the boundary. We use a two-dimensional set of initial conditions that produce all possible trajectories of a particle injected from one opening, and numerically compute the fractal dimension of singular points of a function that maps an initial condition to the number of collisions with the wall before the exit. We introduce a simplified box-counting algorithm, which uses points from a rectangular grid inside the two-dimensional set of the initial conditions, to simplify the calculation, and observe the classical chaotic properties while varying the parameters of the billiard.

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