Chaotic behavior in lemon-shaped billiards with elliptical and hyperbolic boundary arcs - art. no. 016214

Chaotic properties of a new family, ellipse hyperbola billiards (EHB), of l emon-shaped two-dimensional billiards, interpolating between the square and the circle, whose boundaries consist of hyperbolic, parabolic, or elliptic al segments, depending on the shape parameter delta, are investigated class ically and quantally. Classical chaotic fraction is calculated and compared with the quantal level density fluctuation measures obtained by fitting th e calculated level spacing sequences with the Brody, Berry-Robnik, and Berr y-Robnik-Brody distributions. Stability of selected classical orbits is inv estigated, and for some special hyperbolic points in the Poincare sections, the "blinking island" phenomenon is observed. Results for the EHB billiard s are compared with the properties of the family of generalized power-law l emon-shaped billiards.