Fibonacci映射的Teichmüller空间
Teichmüller space of Fibonacci maps
摘要：
根据Sullivan，具有相同组合学（模光滑共轭）的单峰映射的空间${\cal E}$应该被视为无限维的Teichmüller空间。这是沙利文重正化猜想的基本思想。其主要成分之一是为${\cal E}$提供Teichmüller公制。要有这样一个度量，首先必须知道${\cal E}$的所有映射都是拟对称共轭的。对于某些不可重正化映射（当临界点不太常返时），[Ji]和[JS]证明了这一点.在这里，我们考虑一个空间的不可重正单峰映射在某种意义上最快的可能复发的临界点（称为斐波那契）。我们的目标是为这个空间提供Teichmüller度量。
英文摘要：
According to Sullivan, a space ${\cal E}$ of unimodal maps with the same combinatorics (modulo smooth conjugacy) should be treated as an infinitely-dimensional Teichmüller space. This is a basic idea in Sullivan's approach to the Renormalization Conjecture. One of its principle ingredients is to supply ${\cal E}$ with the Teichmüller metric. To have such a metric one has to know, first of all, that all maps of ${\cal E}$ are quasi-symmetrically conjugate. This was proved [Ji] and [JS] for some classes of non-renormalizable maps (when the critical point is not too recurrent). Here we consider a space of non-renormalizable unimodal maps with in a sense fastest possible recurrence of the critical point (called Fibonacci). Our goal is to supply this space with the Teichmüller metric.
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