A+ CATEGORY SCIENTIFIC UNIT

A counterexample to a conjecture of Drużkowski and Rusek

Volume 62 / 1995

Arno van den Essen 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.

Authors

  • Arno van den Essen

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