Absolutely continuous invariant measures for maps with flat tops
Absolutely continuous invariant measures for maps with flat tops
复制标题
平顶地图的绝对连续不变测度
DOI：
10.1007/bf02698845
复制
发表时间：
1989
期刊：
影响因子：
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通讯作者：
M. Misiurewicz
中科院分区：
文献类型：
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作者：
M. Benedicks;M. Misiurewicz
本文旨在作为第二作者论文[M2]的续集。本文的目的是研究在绝对连续不变测度的存在性证明中，在临界点附近何种类型的行为可以代替似多项式行为的问题。所处理的映射类与[M2]中的映射类基本相同，本质上是具有非正Schwartzian导数的分段单调映射，没有汇，临界点的轨迹远离临界点。然而，有一个重要的区别：我们将允许在临界点处的< c flat"行为。一般来说，下面这些额外的条件可以将区间映射到自身
This paper is intended as a sequel to the paper [M2] by the second author. The aim of the paper is to study the problem of knowing what type of behavior near the critical points can replace the polynomial-like behavior in the proof of existence of absolutely continuous invariant measures. The class of mappings treated is basically the same as the one in [M2], essentially piecewise monotone mappings with non-positive Schwartzian derivative, no sinks and trajectories of critical points staying far from the critical points. However there is one important difference: we will allow< c flat" behavior at the critical points. It turns out that generically the following extra conditions on the map/from an interval to itself