论文标题
轨迹和不变措施的编码
Encodings of trajectories and invariant measures
论文作者
论文摘要
我们考虑了同构f产生的紧凑型歧管M上的离散动力系统。令C = {M（i）}为封闭的单元格对M的有限覆盖。动力学系统的符号图像是一个有向图G，其顶点与对应的细胞相对应，在该细胞中，如果图像f（m（i））相交M（j），则弧i和j连接的顶点i和j。我们表明，符号图像的一组路径集合到Tychonoff拓扑中系统的一组轨迹，因为覆盖物的直径往往为零。对于通过不同顶点进行G的周期，从定义上讲，简单的流量是该周期的弧线上的均匀分布。我们表明，随着覆盖物的直径趋于零，简单的流量会趋于弱拓扑中的千古量度。
We consider a discrete dynamical system on a compact manifold M generated by a homeomorphism f. Let C = {M(i)} be a finite covering of M by closed cells. The symbolic image of a dynamical system is a directed graph G with vertices corresponding to cells in which vertices i and j are joined by an arc i to j if the image f(M(i)) intersects M(j). We show that the set of paths of the symbolic image converges to the set of trajectories of the system in the Tychonoff topology as the diameter of the covering tends to zero. For a cycle on G going through different vertices, a simple flow is by definition a uniform distribution on arcs of this cycle. We show that simple flows converge to ergodic measures in the weak topology as the diameter of the covering tends to zero.
