论文标题
偏斜多项式环中的固定点和轨道
Fixed points and orbits in skew polynomial rings
论文作者
论文摘要
我们在一般偏斜的多项式环$ d [x，σ，δ] $中研究多项式的轨道和固定点。我们将第一作者和Vishkautsan的结果扩展到$ d [x] $中的多项式动力学。特别是，我们表明，如果在d $中$ a \ in d $ a \ in d [x，σ，δ] $ cansuse $ f（a）= a $，则$ f^{\ circ n}（a）= a $ for $ f $的每个正式功率。更一般而言，对于多项式$ f $，我们为$ r $ priodic提供了足够的条件。我们的证明是基于由于Lam和Leroy引起的偏斜多项式环的基本结果。
We study orbits and fixed points of polynomials in a general skew polynomial ring $D[x,σ, δ]$. We extend results of the first author and Vishkautsan on polynomial dynamics in $D[x]$. In particular, we show that if $a \in D$ and $f \in D[x,σ,δ]$ satisfy $f(a) = a$, then $f^{\circ n}(a) = a$ for every formal power of $f$. More generally, we give a sufficient condition for a point $a$ to be $r$-periodic with respect to a polynomial $f$. Our proofs build upon foundational results on skew polynomial rings due to Lam and Leroy.
