具有多重断点的重整化双曲性
Hyperbolicity of renormalization for maps with multiple breaks
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中文总结 AI 辅助
本文在断点小且旋转数有界类型的条件下，为多重断点圆周映射构造双曲马蹄，并证明其刚性类为解析子流形。
中文摘要 AI 辅助
我们为具有多重断点型奇点的分段解析圆周同胚构造了双曲马蹄，在旋转数有界类型和有界几何的假设下，只要断点大小一致地小。作为推论，我们获得了此类映射的$C^{1+\alpha}$刚性结果，并证明了刚性类是解析子流形。
英文摘要
We construct hyperbolic horseshoes for piecewise-analytic homeomorphisms of the circle with {\it multiple} break-type singularities, under the assumptions of bounded type rotation numbers and bounded geometry -- provided the sizes of the breaks are uniformly small. As a consequence, we obtain a $C^{1+α}$-rigidity result for such maps and prove that rigidity classes are analytic submanifolds.
