Complexity of trajectories in rectangular billiards
Complexity of trajectories in rectangular billiards
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矩形台球轨迹的复杂性
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Yuliy Baryshnikov
中科院分区：
文献类型：
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作者：
Yuliy Baryshnikov
对于台球在立方体中的轨迹，我们赋予它符号上的连续性--坐标平面的数目序列，轨迹所遇到的面与之平行。轨迹的复杂性是不同的词的长度n发生在它的数量。我们证明，对于一般的轨迹的复杂性是很好的定义和计算，确认猜想Arnoux，Mauduit，Shiokawa和田村[AMST]。
To a trajectory of the billiard in a cube we assign its symbolic trajectory-the sequence of numbers of coordinate planes, to which the faces met by the trajectory are parallel. The complexity of the trajectory is the number of different words of lengthn occurring in it. We prove that for generic trajectories the complexity is well defined and calculate it, confirming the conjecture of Arnoux, Mauduit, Shiokawa and Tamura [AMST].