Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

Details Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

1997-10-31

arxiv.org/abs/chao-dyn/9711001v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 19 pages

Scientific paper

10.1088/0951-7715/11/6/010

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.

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