A counterexample to a conjecture of Drużkowski and Rusek

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Title

Authors ¹

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

d e g F^{- 1} \leq 3^{p - 1}

. We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.

polynomial automorphisms, Jacobian Conjecture

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