Ruelle classical resonances and dynamical chaos: The three- and four-disk scatterers

We study the classical scattering of a point particle on three- and four-disk billiards. The escape dynamics is investigated using the Ruelle classical resonances obtained as the complex poles of the Ruelle ζ functions. The statistical distributions of the real and imaginary parts of the poles as well as their spacings are numerically calculated. Furthermore, we demonstrate the role played by Ruelle’s resonances in the real-time escape processes of an ensemble of classical particles in these scattering systems.