کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4660563 | 1344374 | 2007 | 27 صفحه PDF | دانلود رایگان |
We study forcing of periodic points in orientation reversing twist maps. First, we observe that the fourth iterate of an orientation reversing twist map can be expressed as the composition of four orientation preserving positive twist maps. We then reformulate the problem in terms of parabolic flows, which form the natural dynamics on a certain space of braid diagrams. Second, we focus our attention on period-4 points, which we classify in terms of their corresponding braid diagrams. They can be categorized in two types. If an orientation reversing twist map has a period-4 point of one type, then there is a semi-conjugacy to symbolic dynamics and the system is forced to be chaotic. We also show that this result is sharp in the sense that the remaining type does not necessarily lead to chaos.
Journal: Topology and its Applications - Volume 154, Issue 13, 1 July 2007, Pages 2580-2606