Work

Stable rotation numbers and Birkhoff ordered circles for monotone recurrence relations

Year: 2025

Type: article

Abstract: We study the rotation sets and dynamics of a class of twist maps on the high-dimensional cylinder generated by solutions of monotone recurrence relations. A rotation number is said to be stable if it lies in the rotation sets of all sufficiently close systems. We show that an irrational stable rotation number implies positive topological entropy. As a consequence, each non-wandering orbit has bounded deviations from the corresponding rigid rotation provided the system has zero topological entropy. Furthermore, by introducing Birkhoff ordered circles, we prove Boyland's conjecture in our setting, investigate the realization of rotation numbers defined by invariant measures, and obtain a result of uniformly bounded deviations from the rotation set.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025087

Authors: Bai-Nian Shen, Tong Zhou, Wen-Xin Qin

Institutions: Soochow University, Suzhou University of Science and Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Government of Jiangsu Province, Shuangchuang Program of Jiangsu Province