Break-up of resonant invariant curves in billiards and dual billiards associated to perturbed circular tables
Two area-preserving twist maps are associated to a smooth closed convex table: the (classical) billiard map and the dual billiard map. When the table is circular, these maps are integrable and their phase spaces are foliated by invariant curves. The invariant curves with rational rotation numbers are resonant and do not persist under generic perturbations of the circle. We present a sufficient condition for the break-up of these curves. This condition is expressed directly in terms of the Fourier coefficients of the perturbation. It follows from a standard Melnikov argument.
Abstract A very promising spin physics programme will be soon on the way at the BNL Relativistic Heavy Ion Collider (RHIC). By studying the spin asymmetries for various processes (single photon, single jet and W ± production), we will compare the different predictions obtained using some sets of polarized parton distributions, available in the recent literature. We will put some emphasise on the analysis of the anticipated errors, given the event rates expected from this high luminosity new machine and the current acceptance for the detector systems at RHIC.