单调回复关系中稳定的Farey相邻元与拓扑熵  

Stable Farey neighbors and topological entropy for monotone recurrence relations

作　　者：周同 戴韵洁 陈家敏 杜振洋 ZHOU Tong;DAI Yunjie;CHEN Jiamin;DU Zhenyang(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2024年第2期25-30,共6页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金项目(12201446);江苏省高等学校自然科学研究项目(22KJB110005);江苏省双创博士项目(JSSCBS20220898);大学生创新创业训练计划项目(202310332263X)。

摘　　要：论文旨在利用数论中的Farey相邻元研究高维柱面扭转映射系统的复杂性。鉴于单调回复关系的解和高维柱面扭转映射的轨道之间存在一一对应的关系,问题转化为研究单调回复关系解系统的复杂性。假定单调回复关系的旋转集中有一对稳定的Farey相邻元p/q和p′/q′,利用周期延拓的方法,构造一对交换旋转数p/q和p′/q′的上下解,进而根据Angenent判据,得到系统具有正拓扑熵的结论。Using Farey neighbors in the number theory,this paper studies the complexity of high-dimensional cylinder twist mapping systems.In view of the one-to-one correspondence between solutions of monotone recurrence relations and orbits of high-dimensional cylinder twist mapping,we explored the complexity of solutions of monotone recurrence relations instead.Suppose that there exists a pair of stable Farey neighbors p/q and p′/q′in the rotation set of monotone recurrence relations.A supersolution and a subsolution which exchange rotation numbers p/q and p′/q′are constructed according to the periodic extension method.It then follows from the Angenent’s criterion that the system has positive topological entropy.

关 键 词：旋转集 拓扑熵 Farey相邻元 单调回复关系 高维柱面扭转映射 

分 类 号：O19[理学—数学]