Spectral statistics of a system with sharply divided phase space

We construct a family of non-Kolmogorov-Arnold-Moser (non-KAM) piecewise-linear continuous 2D area-preserving maps which have sharply divided phase space with regions of regular elliptic and chaotic hyperbolic motion. For such systems the shape of the islands of regular motion is either a solid ellipse or a solid polygon, depending on the (ir)rationality of the frequency, and thus the total area of the regular region of phase space can be computed analytically or at least rigorously estimated from below. We analyse the spectral statistics for a few examples of the quantization of our maps, and show that they provide a convenient 'playground' for testing and confirming the key assumptions required for the validity of Berry-Robnik formulae. (author)