论文标题
Babbage功能方程的概括
A generalisation of the Babbage functional equation
论文作者
论文摘要
Kerékjártó的定理的最新完善表明，在$ \ Mathbb r $和$ \ Mathbb r^2 $中\ infty \} $。当$ l \ geq 1 $时，在实际行中，我们证明了$ f^n = f $的解决方案相同的结果，而我们只能在飞机中获得本地版本。通过示例，我们表明，当$ l = 0 $或考虑功能方程式$ f^n = f^k $的情况下，这些结果不再是正确的。
A recent refinement of Kerékjártó's Theorem has shown that in $\mathbb R$ and $\mathbb R^2$ all $\mathcal C^l$-solutions of the functional equation $f^n =\textrm{Id}$ are $\mathcal C^l$-linearizable, where $l\in \{0,1,\dots \infty\}$. When $l\geq 1$, in the real line we prove that the same result holds for solutions of $f^n=f$, while we can only get a local version of it in the plane. Through examples, we show that these results are no longer true when $l=0$ or when considering the functional equation $f^n=f^k$ with $n>k\geq 2$.
