DEGREE GROWTH OF POLYNOMIAL AUTOMORPHISMS AND BIRATIONAL MAPS: SOME EXAMPLES
Résumé
We provide the existence of new degree growths in the context of polynomial automorphisms of C k : if k is an integer ≥ 3, then for any ℓ ≤ k−1 2 there exist polynomial automorphisms f of C k such that deg f n ∼ n ℓ. We also give counterexamples in dimension k ≥ 3 to some classical properties satisfied by polynomial automorphisms of C 2. We provide the existence of new degree growths in the context of birational maps of P k C : assume k ≥ 3; forall 0 ≤ ℓ ≤ k there exist birational maps φ of P k C such that deg φ n ∼ n ℓ .
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