Topologically weakly mixing polygonal billiards. (English) Zbl 1523.37035
The phase space of the billiard within a polygon with all angles being a rational multiple of \(\pi\) is foliated into compact translation surfaces. That is not the case for irrational polygons and it is much less known about billiard dynamics within them.
This paper gives the first known result on higher mixing for the billiard within irrational polygons. It is proved that the billiard map and the corresponding shift obtained by coding billiard orbits by the sequence of sides of the polygon they visit are topologically weakly mixing. The result is obtained using the approximation technique.
This paper gives the first known result on higher mixing for the billiard within irrational polygons. It is proved that the billiard map and the corresponding shift obtained by coding billiard orbits by the sequence of sides of the polygon they visit are topologically weakly mixing. The result is obtained using the approximation technique.
Reviewer: Milena Radnović (Sydney)
MSC:
| 37C83 | Dynamical systems with singularities (billiards, etc.) |
| 37B10 | Symbolic dynamics |
| 37A25 | Ergodicity, mixing, rates of mixing |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
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