论文标题
在赫尔曼戒指和相关杆的时期
On periods of Herman rings and relevant poles
论文作者
论文摘要
研究了可能的赫尔曼环的可能阶段，以至少一个省略的价值，以用于一般的mer态函数。如果杆子被某些含有$ h $的周期的赫尔曼戒指包围，则一根杆子称为$ h $ -relevant，用于herman ring $ h $ $ h $。在本文中，根据$ h $ relevant Poles（例如$ h $）的数量，发现了Herman Ring $ h $ $ p $的下限。更确切地说，只要$ p \ geq \ frac {h（h+1）} {2} $每当$ f^j（h）$（对于某些$ j $）时，围绕着一个极点以及所有省略的$ f $的值。证明在另一种情况下，$ p \ geq \ frac {h（h+3）} {2} $。在相等性的情况下发现足够的条件。还可以证明，如果省略的值包含在不变或两个周期性的FATOU组件中，则该功能没有任何Herman环。
Possible periods of Herman rings are studied for general meromorphic functions with at least one omitted value. A pole is called $H$-relevant for a Herman ring $H$ of such a function $f$ if it is surrounded by some Herman ring of the cycle containing $H$. In this article, a lower bound on the period $p$ of a Herman ring $H$ is found in terms of the number of $H$-relevant poles, say $h$. More precisely, it is shown that $p\geq \frac{h(h+1)}{2}$ whenever $f^j(H)$, for some $j$, surrounds a pole as well as the set of all omitted values of $f$. It is proved that $p \geq \frac{h(h+3)}{2}$ in the other situation. Sufficient conditions are found under which equalities hold. It is also proved that if an omitted value is contained in the closure of an invariant or a two periodic Fatou component then the function does not have any Herman ring.
