BUILDING QUASIMODES IN INTEGRABLE BILLIARDS

It is shown, by means of a simple specific example, that for integrabl e billiards it is possible to build up approximate eigenfunctions, cal led asymptotic eigenfunctions, which, in the semiclassical limit, are concentrated arbitrarily close to a classical periodic orbit and have an arbitrarily long lifetime. These states are directly related to the presence of shell structures in the quantal spectrum of the system. T he results appear to verify a conjecture by Arnold about quasimodes an d provide a method to construct them.