论文标题
非峰图的非理性旋转动力学
Irrational rotation dynamics for unimodal maps
论文作者
论文摘要
本文的第一个结果（定理1.1）是在临界后集合的半偶联图的明确构造，通过（3/5,2/3）$在临界后集的半缀合物构造。我们的构建是米尔诺（Milnor）和lyubich [lm]对斐波那契单峰地图半偶联到圆旋转的构造的概括。在斐波那契图中概括了米尔诺和lyubich的定理，我们证明，我们单峰地图的临界后集合的hausdorff维度为$ 0 $，只要$θ$的持续分数的分解者是$θ$的分解者（theorem 1.2）的（theorem 1.2），或者在theorem 1.2的情况下，就足够了。
The first result of the paper (Theorem 1.1) is an explicit construction of unimodal maps that are semiconjugate, on the post-critical set, to the circle rotation by an arbitrary irrational angle $θ\in(3/5,2/3)$. Our construction is a generalization of the construction by Milnor and Lyubich [LM] of the Fibonacci unimodal maps semi-conjugate to the circle rotation by the golden ratio. Generalizing a theorem by Milnor and Lyubich for the Fibonacci map, we prove that the Hausdorff dimension of the post-critical set of our unimodal maps is $0$, provided the denominators of the continued fraction of $θ$ are bounded (Theorem 1.2) or, in the case of quadratic polynomials, have sufficiently slow growth (Theorem 1.3).
