Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1997-09-03
Nonlinearity 11 (1998), no. 4, 991-1013
Nonlinear Sciences
Chaotic Dynamics
34 pages in LaTeX 2.09 including 8 ps figures (with psfig.tex)
Scientific paper
10.1088/0951-7715/11/4/013
A class of non-compact billiards is introduced, namely the infinite step billiards, i.e., systems of a point particle moving freely in the domain $\Omega = \bigcup_{n\in\N} [n,n+1] \times [0,p_n]$, with elastic reflections on the boundary; here $p_0 = 1, p_n > 0$ and $p_n$ vanishes monotonically. After describing some generic ergodic features of these dynamical systems, we turn to a more detailed study of the example $p_n = 2^{-n}$. What plays an important role in this case are the so called escape orbits, that is, orbits going to $+\infty$ monotonically in the X-velocity. A fairly complete description of them is given. This enables us to prove some results concerning the topology of the dynamics on the billiard.
Esposti Mirko Degli
Lenci Marco
Magno Gianluigi Del
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