论文标题
具有可观察到的可观察到的地图扩展地图的奇异性最大化问题
Ergodic maximization problem for expanding maps with differentiable observables
论文作者
论文摘要
我们表明，对于扩展的地图，在单个周期性轨道上支持了一个通用（开放和密集）$ c^r $（$ r \ in \ mathbb {n} $）的最大程度的度量。 [讨论中存在差距。对于Lipschitz函数的$ c^{\ infty} $近似，我们只能控制$ c^1 $衍生产品，但是我们无法控制$ r \ geq2 $的$ c^r $衍生产品。可能需要使用优雅的近似方法来解决此问题。]
We show that for an expanding map, the maximizing measures of a generic (open and dense) $C^r$ ($r\in\mathbb{N}$) differentiable functions are supported on a single periodic orbit. [There is a gap in the discussions. For the $C^{\infty}$ approximation of the Lipschitz functions, we can only control the $C^1$ derivative, but we can not control the $C^r$ derivatives for $r\geq2$. Elegant approximation methods might be needed to solve this problem.]
