New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure
New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure
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具有西格玛有限绝对连续不变测度的 S-单峰映射的新示例
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Jakobson
中科院分区：
文献类型：
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作者：
J. Al;H. Bruin;M. Jakobson
我们把诱导法和诱导法结合起来
We combine the technique of inducing with a method of
Johnson boxes and construct new examples
of S-unimodal maps $varphi$ which do not have a finite absolutely
continuous invariant measure, but do have a $sigma$-finite one
which is infinite on every non-trivial interval.
We prove the following dichotomy. Every absolutely
continuous invariant measure is either $sigma$-finite, or else it
is infinite on every set of positive Lebesgue measure.