Weakly attracting repellors for piecewise convex maps
Weakly attracting repellors for piecewise convex maps
复制标题
分段凸映射的弱吸引排斥子
DOI：
10.1007/bf03167275
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发表时间：
1992
影响因子：
0.9
通讯作者：
Tomoki Inoue
中科院分区：
文献类型：
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作者：
Tomoki Inoue
本文在一维动力系统中引入了“弱吸引排斥者”的概念，它是一个不稳定的不动点，具有如下性质：不动点与一个点x的迭代之间的“距离”的时间平均几乎对每个点x收敛于0.研究了两类分段凸映射。一类是包含间歇动力系统的分段凸增映射，另一类是与含临界参数的Lorenz方程相关的尖点型映射。给出了分段凸映射具有弱吸引排斥子的条件。我们还研究了具有弱吸引排斥子的分段凸映射的李雅普诺夫数。我们证明的关键是δ-有限不变测度。
We introduce the notion of a “weakly attracting repellor” in one dimensional dynamical systems, which is an unstable fixed point with the following property: the time average of ‘distance’ between the fixed point and the iterates of a pointxconverges to 0 for almost every pointx. We study two classes of piecewise convex maps. One is a class of piecewise convex increasing maps including some intermittent dynamical systems, and the other is a class of cusp type maps which is related to the Lorenz equation with a critical parameter. We give some conditions for a piecewise convex map having a weakly attracting repellor. We also study the Lyapunov numbers of piecewise convex maps with weakly attracting repellors. The key to our proof is a δ-finite invariant measure.