For uniform asymptotically affine(uaa)Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is(uaa)at a point in the train track then the conjugacy is(uaa)everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Cantor sets. We also present similar statements for(uaa)and C~r Markov families.
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机译：对于火车轨道上的统一渐近仿射（uaa）马尔可夫地图，我们证明了以下类型的刚度结果：如果它们之间的拓扑共轭在火车轨道的某个点处（uaa），则该共轭在任何地方。特别地，我们的方法适用于马尔可夫图的域是Cantor集的情况。我们也为（uaa）和C r r马尔科夫族提供类似的陈述。
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