A counterexample to a conjecture of Drużkowski and Rusek
Let F = X + H be a cubic homogeneous polynomial automorphism from to . Let be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that . We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.