论文标题
强烈通勤间隔图
Strongly commuting interval maps
论文作者
论文摘要
如果$ f \ circ g^{ - 1} = g^{ - 1} \ circ f $，映射$ f，g \ colon i \ to i $被称为强烈通勤。我们表明，强烈通勤，分段单调映射$ f，g $可以分解为有限数量的不变间隔（或2个时期间隔），$ f，g $既可以是打开的地图，否则至少是单调的。结果，我们表明强烈通勤分段单调间隔图具有共同的固定点。本文的结果也对理解某些地图的动力学特性在反极限空间上有影响。
Maps $f,g\colon I\to I$ are called strongly commuting if $f\circ g^{-1}=g^{-1}\circ f$. We show that strongly commuting, piecewise monotone maps $f,g$ can be decomposed into a finite number of invariant intervals (or period 2 intervals) on which $f,g$ are either both open maps, or at least one of them is monotone. As a consequence, we show that strongly commuting piecewise monotone interval maps have a common fixed point. Results of the paper also have implications in understanding dynamical properties of certain maps on inverse limit spaces.
