论文标题
朱莉娅（Julia
Julia sets with Ahlfors-regular conformal dimension one
论文作者
论文摘要
对于批判性有限的双曲合理地图$ f $，我们表明朱莉娅集合$ \ mathcal {j} _f $具有ahlfors-refformal尺寸一个，并且仅当f是钩编织图，即，即$ f $ invariant Graph contripation $ f $ invariant Graph包含$ f polication $ f的$ f zer tobolation $ f zer zer topitogity $ f | _g pote toptoical topitogity $ f pote toptogical toberial。我们使用有限的细分规则来获得图形虚拟内态性，这是对后有限的有限理性地图的一维简化，并近似图形虚拟内态的渐变形成式共形能量，以估算AHLFORS期权的正形尺寸。特别是，我们提出了一个减少有限细分规则的想法，并证明在理性地图的分解下，渐近保形能量的单调性。
For a post-critically finite hyperbolic rational map $f$, we show that the Julia set $\mathcal{J}_f$ has Ahlfors-regular conformal dimension one if and only if f is a crochet map, i.e., there is an $f$-invariant graph G containing the post-critical set such that $f|_G$ has topological entropy zero. We use finite subdivision rules to obtain graph virtual endomorphisms, which are 1-dimensional simplifications of post-critically finite rational maps, and approximate the asymptotic conformal energies of the graph virtual endomorphisms to estimate the Ahlfors-regular conformal dimensions. In particular, we develop an idea of reducing finite subdivision rules and prove the monotonicity of asymptotic conformal energies under the decomposition of rational maps.
