We study endomorphisms constructed by Sarah Koch in her thesis and we focus on the eigenvalues of differential such maps at its fixed points. In Koch's thesis, to each post-critically finite unicritical polynomial, associated a algebraic endomorphism $\mathbb{CP}^k$. showed that differentials along periodic cycles outside post-critical sets have modulus strictly greater than $1$. this article, ...

It is shown that for any sufficiently regular even Minkowski valuation Φ which homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball, where balls are only solutions to fixed-point problem Φ2K=αK. This significantly generalizes results by Ivaki projection bodies suggests, via Lutwak–Schneider class reduction technique, new approach Petty's conjectured inequality.

Abstract This short note is on the question whether intersection of all fixed points a positive arithmetic operator and its closed can proved to be equivalent in weak fragment second order arithmetic.