A counterexample to a conjecture of Drużkowski and Rusek
Volume 62 / 1995
Annales Polonici Mathematici 62 (1995), 173-176
DOI: 10.4064/ap-62-2-173-176
Abstract
Let F = X + H be a cubic homogeneous polynomial automorphism from $ℂ^n$ to $ℂ^n$. Let $p$ be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that $deg F^{-1} ≤ 3^{p-1}$. We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.
