论文标题
测量最大化KAN内态熵
Measures maximizing the entropy for Kan endomorphisms
论文作者
论文摘要
1994年，Ittai Kan提供了第一个与盆地混合的地图的例子。 KAN示例对应于在表面上定义的部分双曲内形态性，边界表现出两个相互融合的双曲物理测量。这两种措施都在边界上支持，并且也是衡量最大化拓扑熵的测量。在这项工作中，我们证明了圆柱体内部支持的第三个双曲线度量的存在，该测量最大化了包括KAN示例在内的较大类图的熵。我们还证明了这一说法，用于大型大型地图的大型不变度度量，包括KAN示例的扰动。
In 1994, Ittai Kan provided the first examples of maps with intermingled basins. The Kan example corresponds to a partially hyperbolic endomorphism defined on a surface with the boundary exhibiting two intermingled hyperbolic physical measures. Both measures are supported on the boundary, and they are also measures maximizing the topological entropy. In this work, we prove the existence of a third hyperbolic measure supported in the interior of the cylinder that maximizes the entropy for a larger class of maps including the Kan example. We also prove this statement for a larger class of invariant measures of large class maps including perturbations of the Kan example.
