论文标题
关于Mather的$β$ - 标准式扭曲图的规律性
On the regularity of Mather's $β$-function for standard-like twist maps
论文作者
论文摘要
我们考虑了保留环形图的区域的最小平均作用（马瑟的$β$函数）。此功能的规律性属性与系统动力学共享有趣的关系。我们证明，与标准式扭曲图相关的$β$函数承认了一个唯一的$ C^1 $ -HOLOLOMORMORPHIC COMPLEX EXTENSION，它与此功能在一组真实的双磷频频率上相吻合。
We consider the minimal average action (Mather's $β$ function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the $β$-function associated to a standard-like twist map admits a unique $C^1$-holomorphic complex extension, which coincides with this function on the set of real diophantine frequencies.
