For a class of piecewise convex maps f on the interval $[0,1]$, we show that f has a unique absolutely continuous invariant probability measure μ with exponential decay of correlations, and we also present the explicit upper bounds on the rate. Moreover, we show the exponential loss of memory for a sequential dynamical system consisting of piecewise convex maps.

中文翻译：

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Lasota-Yorke 凸图的相关性衰减和记忆丧失

对于区间上的一类分段凸图f$[0,1]$，我们表明f具有唯一的绝对连续不变概率度量μ，相关性呈指数衰减，并且我们还给出了速率的显式上限。此外，我们展示了由分段凸图组成的顺序动态系统的内存指数损失。