发表机构
University of Banja Luka（班亚卢卡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为交换圆微分同胚对定义重整化算子，在加速Brun算法驱动下，证明对有界型旋转向量指数快速收敛到刚性旋转，并推广到满测度类，同时证明算子拓扑双曲性。
AI 中文摘要
我们为$C^3$类的交换保向圆微分同胚对定义了一个重整化算子。该算子由加速Brun多维连分数算法驱动。对于同时有界型的旋转向量，在由所有最终周期型且具有Pisot周期矩阵所满足的可和强收敛条件下，重整化在$C^2$中指数快速收敛到刚性旋转对。该对同时$C^{1+\gamma}$共轭于旋转对，其中$\gamma>0$仅依赖于有界型常数。快速重整化将指数收敛和$C^1$刚性推广到一类具有完全Lebesgue测度的旋转向量，其中包含有界型之外的显式向量。我们证明该算子是拓扑双曲的。按旋转向量对重整化对的分割是一个不变层状结构，其叶片是拓扑共轭类。所有结果对$C^{2+\alpha}$类的对成立。
英文摘要
We define a renormalization operator for pairs of commuting orientation preserving circle diffeomorphisms of class $C^3$. The operator is driven by the accelerated Brun multidimensional continued fraction algorithm. For rotation vectors of simultaneously bounded type, under a summable strong convergence condition satisfied by all eventually periodic types with Pisot period matrix, the renormalizations converge exponentially fast in $C^2$ to pairs of rigid rotations. The pair is simultaneously $C^{1+γ}$ conjugate to the pair of rotations, with $γ>0$ depending only on the bounded type constant. A fast renormalization extends exponential convergence and $C^1$ rigidity to a class of rotation vectors of full Lebesgue measure, containing explicit vectors outside bounded type. We show that the operator is topologically hyperbolic. The partition of the renormalized pairs by rotation vector is an invariant lamination whose leaves are the topological conjugacy classes. All results hold for pairs of class $C^{2+α}$.
