Memory Maps with Elliptical Trajectories

Ted Szylowiec, Pawel Góra
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引用次数: 0

Abstract

A family of maps with memory, parameterized by [Formula: see text], is shown to have either periodic trajectories or dense trajectories on ellipses which support absolutely continuous invariant measures. Furthermore, for [Formula: see text], i.e. [Formula: see text] with [Formula: see text] and [Formula: see text], all points except [Formula: see text] either go into a polygonal region centered at [Formula: see text] if [Formula: see text] is rational, or are attracted to an elliptical region having the same center, if [Formula: see text] is irrational. In the polygonal case, we examine a mechanism for the appearance of islands supporting absolutely continuous invariant measures.
椭圆轨迹的记忆映射
一组具有记忆的映射,参数化为[公式:见文本],被证明在支持绝对连续不变测度的椭圆上具有周期轨迹或密集轨迹。此外,对于[公式:见文],即[公式:见文]与[公式:见文]和[公式:见文],如果[公式:见文]是有理的,则除[公式:见文]外的所有点要么进入以[公式:见文]为中心的多边形区域,要么被吸引到具有相同中心的椭圆区域,如果[公式:见文]是非理性的。在多边形情况下,我们研究了支持绝对连续不变测度的岛屿出现的机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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