长分支斯特姆单峰映射的绝对连续不变测度与Collet-Eckmann条件
Absolutely continuous invariant measures and the Collet-Eckmann condition for long-branched Sturmian unimodal maps
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中文总结 AI 辅助
该研究聚焦长分支斯特姆单峰映射，通过揉类与特定洛伦兹构造的关联，计算切割共切割时间，建立绝对连续不变测度判据，还证明几乎所有旋转角下无有限阶S-单峰实现满足Collet-Eckmann条件。
中文摘要 AI 辅助
我们研究分支序列对应揉映射值序列为斯特姆字的长分支单峰映射，将这类揉类与Anušić、Bruin和Činč的发育不全洛伦兹构造产生的揉类等同，其二次型代表与Blé从刚性旋转构造的映射等同。我们显式计算切割时间与共切割时间，建立绝对连续不变概率测度存在性与不存在性的判据，还证明对勒贝格几乎所有旋转角，不存在有限阶S-单峰实现满足Collet-Eckmann条件。
英文摘要
We study long-branched unimodal maps for which the sequence of values of the kneading map form a Sturmian word. We identify these kneading classes with those arising from the stunted Lorenz construction of Anušić, Bruin, and Činč, and their quadratic representatives with the maps constructed by Blé from rigid rotations. We compute the cutting and co-cutting times explicitly and establish criteria for the existence and nonexistence of absolutely continuous invariant probability measures. We also show that, for Lebesgue-almost every rotation angle, no finite-order $S$-unimodal realization satisfies the Collet-Eckmann condition.
