ABSTRACT

For a class of piecewise convex maps T with an indifferent fixed point and critical points on the interval $[0,1]$, we show that T has a unique absolutely continuous invariant probability measure μ, and the invariant density has a upper bound and a lower bound. The Frobenius–Perron operator of T is asymptotically stable. We also obtain the polynomial decay rate of correlations with respect to μ by using the probabilistic method proposed by Liverani, Saussol and Vaienti.

中文翻译：

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具有临界点的间歇图的不变密度

摘要

对于一类分段凸图T，在区间上具有不变的固定点和临界点$[0，\mathrm{1个}]$，我们证明T具有唯一的绝对连续不变概率度量μ，且不变密度具有上限和下限。T的Frobenius-Perron算子是渐近稳定的。我们还使用Liverani，Saussol和Vaienti提出的概率方法，获得了与μ相关的多项式衰减率。