Ρ-bounded orbits and Arnold tongues for quasiperiodically forced circle maps*Supported by the National Natural Science Foundation of China (11771316, 11790274 and 12171347). (18th January 2022)

• Record Type: Journal Article
• Authors: Zhou, Tong; Hu, Wen-Juan; Huang, Qi-Ming; Qin, Wen-Xin
• Is Part Of: Nonlinearity. Volume 35:Number 3(2022)
• Page Start: 1119
• Page End: 1130
• Publication Date: 2022-01-18
• Subjects: quasiperiodically forced circle map -- ρ-bounded orbit -- fibred rotation interval -- Arnold tongue; 37B55 -- 37C65 -- 37E45; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac473d
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: For quasiperiodically forced (qpf) continuous circle maps with degree one, the set of fibred rotation numbers is a closed interval or a singleton. We show in this paper that if a number ρ is in the interior of this interval, then there exist ρ -bounded orbits. We also discuss extensions of the structure of Arnold tongues for qpf circle homeomorphisms to qpf continuous circle maps with degree one.