Abundance of Mode-Locking for Quasiperiodically Forced Circle Maps

作者：Wang, J.^*; Jaeger, T.

来源：Communications in Mathematical Physics, 2017, 353(1): 1-36.

DOI：10.1007/s00220-017-2870-5

• STRANGE NONCHAOTIC ATTRACTORS
• POSITIVE LYAPUNOV EXPONENT
• CANTOR SPECTRUM
• MINIMALITY
• ARNOLD

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 -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 -cocycles by Young and Bjerklov. The methods apply to a variety of examples, including a forced version of the classical Arnold circle map.

• 出版日期2017-7
• 单位南京理工大学