Scar functions in the Bunimovich Stadium billiard

Details Scar functions in the Bunimovich Stadium billiard Scar functions in the Bunimovich Stadium billiard

2002-04-23

arxiv.org/abs/nlin/0204055v2

Nonlinear Sciences

Chaotic Dynamics

21 pages, 10 figures

Scientific paper

10.1088/0305-4470/35/38/301

In the context of the semiclassical theory of short periodic orbits, scar functions play a crucial role. These wavefunctions live in the neighbourhood of the trajectories, resembling the hyperbolic structure of the phase space in their immediate vicinity. This property makes them extremely suitable for investigating chaotic eigenfunctions. On the other hand, for all practical purposes reductions to Poincare sections become essential. Here we give a detailed explanation of resonances and scar functions construction in the Bunimovich stadium billiard and the corresponding reduction to the boundary. Moreover, we develop a method that takes into account the departure of the unstable and stable manifolds from the linear regime. This new feature extends the validity of the expressions.

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