Topological conditions for the existence of invariant measures for unimodal maps
Topological conditions for the existence of invariant measures for unimodal maps
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单峰映射不变测度存在的拓扑条件
DOI：
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发表时间：
1994
影响因子：
0.9
通讯作者：
H. Bruin
中科院分区：
文献类型：
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作者：
H. Bruin
摘要本文给出了一类具有不变测度的S-单峰映射，该不变测度关于Lebesgue测度是绝对连续的。这个测度常常可以被证明是有限的。我们给出了一个例子的地图，它有这样一个有限的措施，并为其中的liminf的衍生物的迭代的地图在临界值是有限的。证明了所有拓扑共轭的非平坦S-单峰映射都具有相同的性质。
Abstract We present a class of S-unimodal maps having an invariant measure which is absolutely continuous with respect to Lebesgue measure. This measure can often be proved to be finite. We give an example of a map which has such a finite measure and for which the lim inf of the derivatives of the iterates of the map in the critical value is finite. It will be shown that all topologically conjugate non-flat S-unimodal maps have the same properties.