Geodesic
A counterexample to a conjecture of Drużkowski and Rusek
Annales Polonici Mathematici, Tome 62 (1995) no. 2, pp. 173-176
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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.
DOI : 10.4064/ap-62-2-173-176
Mots-clés : polynomial automorphisms, Jacobian Conjecture 
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Arno van den Essen. A counterexample to a conjecture of Drużkowski and Rusek. Annales Polonici Mathematici, Tome 62 (1995) no. 2, pp. 173-176. doi: 10.4064/ap-62-2-173-176

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