Birkhoff Orbits for Twist Homeomorphisms on the High-Dimensional Cylinder  

高维柱面上的扭转同胚的Birkhoff轨道

作　　者：ZHOU Tong 周同(苏州科技大学数学科学学院,江苏苏州215009)

机构地区：[1]School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China

出　　处：《Wuhan University Journal of Natural Sciences》2025年第1期43-48,共6页武汉大学学报(自然科学英文版)

基　　金：Supported by the National Natural Science Foundation of China(12201446);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005);the Shuangchuang Program of Jiangsu Province(JSSCBS20220898)。

摘　　要：It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.单调回复关系可以诱导一族高维柱面上的扭转同胚,它们是环域或二维柱面上单调扭转映射的推广。本文通过构造单调回复关系的有界解,获得如下的主要结论:如果诱导同胚有一个紧致的正向不变集,那么它有Birkhoff轨道。因此,本文推广了Angenent在低维情形的结果。

关 键 词：monotone recurrence relation twist homeomorphism high-dimensional cylinder bounded action Birkhoff orbit 

分 类 号：O19[理学—数学]