论文标题
两次圆形图的重新归一化
Renormalization of bicritical circle maps
论文作者
论文摘要
在许多重要情况下已经建立的重新规定理论的一般安萨兹（Ansatz）指出，指数融合轨道的指数收敛意味着拓扑结合实际上是平稳的（仅限于原始系统的吸引子时）。在本文中，我们为一大类的两类双圆图建立了此原理，该图是$ c^3 $圆形同构具有非理性旋转数，正好是两个（非静电）关键点。此处提供的证据是对双临界和德·梅洛（De Faria）和de Melo的一种适应性的改编。当与最近的一些论文结合使用时，我们的主要定理意味着用于实现的双临界圆形图的$ c^{1+α} $刚性具有有界类型的旋转数。
A general ansatz in Renormalization Theory, already established in many important situations, states that exponential convergence of renormalization orbits implies that topological conjugacies are actually smooth (when restricted to the attractors of the original systems). In this paper we establish this principle for a large class of bicritical circle maps, which are $C^3$ circle homeomorphisms with irrational rotation number and exactly two (non-flat) critical points. The proof presented here is an adaptation, to the bicritical setting, of the one given by de Faria and de Melo for the case of a single critical point. When combined with some recent papers, our main theorem implies $C^{1+α}$ rigidity for real-analytic bicritical circle maps with rotation number of bounded type.
