Geometrical origin of chaoticity in the bouncing ball billiard
arXiv:1003.2505 · doi:10.1016/j.chaos.2011.10.002
Abstract
We present a study of the chaotic behavior of the bouncing ball billiard. The work is realised on the purpose of finding at least certain causes of separation of the neighbouring trajectories. Having in view the geometrical construction of the system, we report a clear origin of chaoticity of the bouncing ball billiard. By this we claim that in case when the floor is made of arc of circles - in a certain interval of frequencies - a lower bound for the maximal Ljapunov can be evaluated by sem-ianalitical techniques.
We plan to publish this manuscript in a regular journal soon.
References in corpus (6)
- Back to balls in billiards
- Viscosity in the escape-rate formalism
- Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals
- Chaotic dynamics in a simple bouncing ball model
- Spiral modes in the diffusion of a granular particle on a vibrating surface
- Relating chaos to deterministic diffusion of a molecule adsorbed on a surface