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Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation with a fixed step length and; (ii) random movement around the boundary. After injecting an ensemble of particles through the hole we show that the surviving probability of the particles without recurring - without escaping - from the billiard is described by an exponential law and that the slope of the decay is proportional to the relative size of the hole. Since the phase space of the system exhibits islands of stability we show that there are preferred regions of escaping in the polar angle, hence given a partial answer to an open problem: {it Where to place a hole in order to maximize or minimize a suitable defined measure of escaping}.
We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the particles
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the energy regime
In generic Hamiltonian systems with a mixed phase space chaotic transport may be directed and ballistic rather than diffusive. We investigate one particular model showing this behaviour, namely a spatially periodic billiard chain in which electrons m
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous work on gravi
We study the collision between the cue and the ball in the game of billiards. After studying the collision process in detail, we write the (rotational) velocities of the ball and the cue after the collision. We also find the squirt angle of the ball