RESEARCH ANNOUNCEMENT: STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS UNDER WEAK HYPERBOLICITY ASSUMPTIONS
RESEARCH ANNOUNCEMENT: STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS UNDER WEAK HYPERBOLICITY ASSUMPTIONS
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研究公告：弱双曲线假设下一维地图的统计特性
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
W. Shen
中科院分区：
文献类型：
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作者：
Juan RIVERA;Weixiao SHENddagger;W. Shen
动力系统理论中的一个普遍问题是描述给定系统的大多数轨迹的渐近行为。从概率的角度来看，如果几乎所有轨迹的渐近分布都是由许多不变的概率测度描述的，并且具有良好的几何和统计性质，则动力系统是很好理解的。这种方法已经普及了俄罗斯学校自20世纪60年代以来，它已成功地应用于一致双曲动力系统的开创性工作西奈，Ruelle和Bowen [Sin 72，Rue 76，Bow 75]。将这些结果推广到非一致双曲动力系统一直是，并将继续是，动力系统研究的主要主题之一。在本文中，我们宣布的结果存在的物理措施及其几何和统计性质的一个大类的真实的和复杂的一维地图。给定一个作用在紧度量空间X上的连续映射f：X arrow X，给出了一个不变的概率Borcl测度
u$被称为cd $rni$.ring，如果对于所有的$varphi，$ $psiin$
A general problem in the theory of dynamical systems is to describe the asymptotic behavior of most trajectories of a given system. From a probabilistic point of view, a dynamical system is well understood if the asymptotic distribution of almost all trajectories is described by finitely many invariant probability measures, with good geometric and statistical properties. Such an approach has been popularized by the Russian school since the $1960s$ and it has been successfully applied to uniformly hyperbolic dynamical systems by the pioneering work of Sinai, Ruelle, and Bowen [Sin72, Rue76, Bow75]. To generalize these results to non-uniformly hyperbolic dynamical systems has been, and continues to be, one of the main themes of research on dynamical systems. In this paper, we announce results on existence of physical measures and their geometric and statistical properties for a large class of real and complex one-dimensional maps. Given a continuous map $f$ : $Xarrow X$ acting on a compact metric space $X$ , an invariant probability Borcl measure $
u$ is callcd $rni$.ring, if for all $varphi,$ $psiin$