非不变平面连续统中的不动点
Fixed points in non-invariant plane continua
摘要：
如果具有$a<b$的$f:[a,b]\to \mathbb{R}$是连续的，并且使得$a$和$b$被$f$在相反方向上映射，则$f$在$I$中具有不动点。设$f:\mathbb{C}\to\mathbb{C}$是映射，$X$是连续统.我们扩展了上述某些连续映射的树突$X\to D, X\subset D$和正向映射$f:X\to \mathbb{C}, X\subset \mathbb{C}$与连续$X$不一定不变。然后证明了在某些情形下，全纯映射$f:\mathbb{C}\to\mathbb{C}$在连续统$X$中必有不动点$a$，使得$a\in \mathrm{Int}(X)$或$f$在$a$处旋转.
英文摘要：
If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend the above for certain continuous maps of dendrites $X\to D, X\subset D$ and for positively oriented maps $f:X\to \mathbb{C}, X\subset \mathbb{C}$ with the continuum $X$ not necessarily invariant. Then we show that in certain cases a holomorphic map $f:\mathbb{C}\to\mathbb{C}$ must have a fixed point $a$ in a continuum $X$ so that either $a\in \mathrm{Int}(X)$ or $f$ exhibits rotation at $a$.
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