正则图和半正则图的球面吸引子
Spherical Averages on Regular and Semiregular Graphs
摘要：
1966年，P. Guenther证明了如下结果：给定常曲率紧致曲面M上的连续函数f及其到泛覆盖双曲平面的周期提升g，则提升g在递增球面上的平均值收敛于函数f在曲面M上的平均值。在这篇文章中，我们证明了类似的结果，对函数的顶点和边的正则和半正则图，特别强调的收敛速度。我们还考虑了更一般的集合，如弧，管和horocycles的平均值。
英文摘要：
In 1966, P. Guenther proved the following result: Given a continuous function f on a compact surface M of constant curvature -1 and its periodic lift g to the universal covering, the hyperbolic plane, then the averages of the lift g over increasing spheres converge to the average of the function f over the surface M. In this article, we prove similar results for functions on the vertices and edges of regular and semiregular graphs, with special emphasis on the convergence rate. We also consider averages over more general sets like arcs, tubes and horocycles.
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