MathOverflow

A version of the Lebesgue Differentiation theorem states that if $f \in L^1_{\mathrm{loc}}(\mathbb{R}^n)$, then\begin{equation}\lim_{r \to 0} \frac{1}{|B_r(x)|}\int_{B_{r}(x)} f(y) \, \mathrm{d}y = f(x)\end{equation}for almost every $x \in \mathbb{R...

Let $A$ be a commutative ring. Following Hazewinkel Operations in the K-Theory of Endomorphisms, the ring of rational Witt vectors (that is, the ring of big Witt vectors which are rational functions) can be interpreted as representing classes of endomorphisms...

Question: I am interested in the dynamics of entire functions. How does one find the images of the Fatou and the Julia set of an entire function? What is the well-known software for this?In particular, what is the image of the Fatou set of $f(z)=e^{z...

Let $k$ be an arbitrary field, and $A,B,A',B'\in M_n(k)$. Do we have any algorithm with polynomial complexity to determine the simultaneous similarity of the pair $(A,B)$ with $(A',B')$?
I found the paper Friedman - Simultaneous similarity of matrices which solved the case when $k=\mathbb{C}$. Do we have similar results when $k$ is another field?...