论文标题
通过统计不稳定的非统计行为：非统计的Anosov-Katok差异性
Non-statistical behavior via Statistical instability: Non-statistical Anosov-Katok diffeomorphisms
论文作者
论文摘要
\ textIt {非统计动力学}是那些具有积极度量的点的集合（W.R.T.的参考概率度量，在大多数示例中，lebesgue在歧管上）都没有经验度量的收敛顺序。在本文中，我们表明在非统计动力学的存在背后，还有其他一些动力学属性：\ textit {统计不稳定性}。为此，我们介绍了统计稳定性和不稳定性概念的一般形式化，并在动态系统的一部分上引入足够的条件，以在统计不稳定方面包含非统计图。我们遵循这一想法，并在环形的Anasov-Katok差异范围内引入了一类新的非统计图。
\textit{Non-statistical dynamics} are those for which a set of points with positive measure (w.r.t. a reference probability measure which is in most examples the Lebesgue on a manifold) do not have a convergent sequence of empirical measures. In this paper, we show that behind the existence of non-statistical dynamics, there is some other dynamical property: \textit{statistical instability}. To this aim, we present a general formalization of the notions of statistical stability and instability and introduce sufficient conditions on a subset of dynamical systems to contain non-statistical maps in terms of statistical instability. We follow this idea and introduce a new class of non-statistical maps in the space of Anasov-Katok diffeomorphisms of the annulus.
