Abundance of Mode-Locking for Quasiperiodically Forced Circle Maps
 作者： J. Wang,  T. Jäger 作者单位： 1Nanjing University of Science and Technology2Institute of Mathematics, Friedrich-Schiller-University Jena 刊名： Communications in Mathematical Physics, 2017, Vol.353 (1), pp.1-36 来源数据库： Springer Nature Journal DOI： 10.1007/s00220-017-2870-5 英文摘要： We study the phenomenon of mode-locking in the context of quasiperiodically forced non-linear circle maps. As a main result, we show that under certain $${\mathcal{C}^1}$$ -open condition on the geometry of twist parameter families of such systems, the closure of the union of mode-locking plateaus has positive measure. In particular, this implies the existence of infinitely many mode-locking plateaus (open Arnold tongues). The proof builds on multiscale analysis and parameter exclusion methods in the spirit of Benedicks and Carleson, which were previously developed for quasiperiodic $${{\rm SL}(2,\mathbb{R})}$$ -cocycles by Young and Bjerklöv. The methods apply to a variety of examples, including a forced version of the classical Arnold circle map. 原始语种摘要： We study the phenomenon of mode-locking in the context of quasiperiodically forced non-linear circle maps. As a main result, we show that under certain $${\mathcal{C}^1}$$ -open condition on the geometry of twist parameter families of such systems, the closure of the union of mode-locking plateaus has positive measure. In particular, this implies the existence of infinitely many mode-locking plateaus (open Arnold tongues). The proof builds on multiscale analysis and parameter exclusion methods in the spirit of Benedicks and Carleson, which were previously developed for quasiperiodic $${{\rm SL}(2,\mathbb{R})}$$ -cocycles by Young and Bjerklöv. The methods apply to a variety of examples, including a forced version of the classical Arnold circle map.

• multiscale　通用换算
• circle
• twist　扭转
• locking　同步
• forced　被迫
• apply　应用
• parameter　参数
• proof　证明
• quasiperiodic　准周期的
• infinitely　无限地