2017/12/07 by Zhiyuan Zhang, Zhang, Zhiyuan · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1712.02481
arxiv created 2017/12/07 · arxiv updated 2017/12/08
We study the circle homeomorphisms extensions over a strictly ergodic homeomorphism. Under a very mild restriction, we show that the fibered rotation number is locally constant on an open and dense subset. In the complement of this set, we found a dense subset in which every map is conjugate to a direct product. Our result provides a generalisation of Avila-Bochi-Damanik's result on \rm SL(2,ℝ)-cocycles, and Jager-Wang-Zhou's result on quasi-periodically forced maps, to a broader setting.