Parabolic dynamics and anisotropic Banach spaces
Parabolic dynamics and anisotropic Banach spaces
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抛物线动力学和各向异性巴纳赫空间
DOI：
10.4171/jems/892
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发表时间：
2014
影响因子：
2.6
通讯作者：
C. Liverani
中科院分区：
文献类型：
--
作者：
P. Giulietti;C. Liverani
我们研究了抛物线流遍历平均值研究中出现的分布（例如 Flaminio-Forni 的工作中）与双曲动力系统统计特性研究中出现的分布（即传递算子的特征分布）之间的关系。为了尽可能避免影响基本思想的技术问题，我们将自己限制在环面上的简单流程。我们的主要结果是，粗略地说，抛物线流的遍历平均值的增长是由与重正化动力学相关的合适传递算子的特征值控制的。我们所阐述的概念联系预计具有相当的普遍性。
We investigate the relation between the distributions appearing in the study of ergodic averages of parabolic flows (e.g. in the work of Flaminio-Forni) and the ones appearing in the study of the statistical properties of hyperbolic dynamical systems (i.e. the eigendistributions of the transfer operator). In order to avoid, as much as possible, technical issues that would cloud the basic idea, we limit ourselves to a simple flow on the torus. Our main result is that, roughly, the growth of ergodic averages of a parabolic flows is controlled by the eigenvalues of a suitable transfer operator associated to the renormalising dynamics. The conceptual connection that we illustrate is expected to hold in considerable generality.