论文标题
无限r型单峰图周期点的统计特性
Statistical properties of periodic points for infinitely renormalizable unimodal maps
论文作者
论文摘要
对于带有非固定临界点的无限型施瓦茨单峰地图$ f $ f $，我们分析周期点的统计特性，因为周期往往是无穷大的。引入重量函数$φ$，是连续或几何电位$φ=-β\ log | f'| $（$β\ in \ mathbb r $），我们为加权周期点建立了2级大偏差原理。由此，我们推断出所有加权周期点相对于潜在$φ$的平衡状态等分。特别是，随之而来的是，所有周期点都相对于最大熵的度量进行了等分，并且所有周期点都与其Lyapunov指数加权的所有周期点相对于在吸引吸引的Cantor集中支持的临界后措施而言。
For an infinitely renormalizable negative Schwarzian unimodal map $f$ with non-flat critical point, we analyze statistical properties of periodic points as the periods tend to infinity. Introducing a weight function $φ$ which is a continuous or a geometric potential $φ=-β\log|f'|$ ($β\in\mathbb R$), we establish the level-2 Large Deviation Principle for weighted periodic points. From this, we deduce that all weighted periodic points equidistribute with respect to equilibrium states for the potential $φ$. In particular, it follows that all periodic points are equidistributed with respect to measures of maximal entropy, and all periodic points weighted with their Lyapunov exponents are equidistributed with respect to the post-critical measure supported on the attracting Cantor set.
