Abundance of Mode-Locking for Quasiperiodically Forced Circle Maps
作者: J. WangT. Jäger
作者单位: 1Nanjing University of Science and Technology
2Institute 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.
全文获取路径: Springer Nature  (合作)
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影响因子:1.971 (2012)

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关键词翻译
关键词翻译
  • 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