Mathematics

CLC number: O19

Birkhoff Orbits for Twist Homeomorphisms on the High-Dimensional Cylinder

高维柱面上的扭转同胚的 Birkhoff 轨道

School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China

Received: 28 January 2024

Abstract

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.

摘要

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。