Abstract
Dynamical properties of the parabolic oval and elliptical stadium billiards are investigated analytically and numerically. These systems exhibit integrable, mixed or fully chaotic behavior, dependent on the shape parameters. In the elliptical stadium, where our shape parameters are δ and λ, calculations confirm the existence of a large fully chaotic region surrounding the straight line δ = 1 − λ in the parameter space, corresponding to the Bunimovich stadium billiard. The region δ < 1 − λ with elongated semiellipses has been previously discussed. Here we discuss the results of analysis of diametral orbits of period two, the hourglass and diamond orbits of period four, and a family of multidiamond orbits of higher periods, as well as the possible predictions for behavior of the leaking billiards of the same type. The quantal statistical properties of the elliptical stadium billiard are also discussed.
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