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) - Zhou, Tong; Hu, Wen-Juan; Huang, Qi-Ming; Qin, Wen-Xin
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.