Limited to Ergodic Bil l iards
نویسنده
چکیده
Abs t rac t , Sufficient conditions are found so that a family of smooth Hamiltonian flows limits to a billiard flow as a parameter e --~ 0. This limit is proved to be C 1 near non-singular orbits and C o near orbits tangent to the billiard boundary. These results are used to prove that scattering (thus ergodic) billiards with tangent periodic orbits or tangent homoclinic orbits produce nearby Hamiltonian flows with elliptic islands. This implies that ergodicity may be lost for smooth potentials which are arbitrarily close to ergodic billiards. Thus, in some cases, anomoulous transport associated with stickiness to stability islands is expected
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