Spectral properties and anomalous transport in a polygonal billiard

We analyze a class of polygonal billiards, whose behavior is conjectured to exhibit a variety of interesting dynamical features. Correlation functions are numerically investigated, and in a subclass of billiard tables they gi ve indications about a singular continuous spectral measure. By lifting bil liard dynamics we are also able to study transport properties: the (normal or anomalous) diffusive behavior is theoretically connected to a scaling in dex of the spectral measure; the proposed identity is shown to agree with n umerical simulations. (C) 2000 American Institute of Physics. [S1054-1500(0 0)01901-7].