Statistical properties for an open oval billiard: An investigation of the escaping basins

Abstract

Statistical properties for recurrent and non recurrent escaping particles in an oval billiard with holes in the boundary are investigated. We determine where to place the holes and where to launch particles in order to maximize or minimize the escape measurement. Initially, we introduce a fixed hole in the billiard boundary, injecting particles through the hole and analyzing the survival probability of the particles inside of the billiard. We show there are preferential regions to observe the escape of particles. Next, with two holes in the boundary, we obtain the escape basins of the particles and show the influence of the stickiness and the small chains of islands along the phase space in the escape of particles. Finally, we discuss the relation between the escape basins boundary, the uncertainty about the boundary points, the fractal dimension of them and the so called Wada property that appears when three holes are introduced in the boundary.