We characterize the polynomial automorphisms of $C^3,$ which commute with a regular automorphism. We use their meromorphic extension to $P^3$ and consider their dynamics on the hyperplane at infinity. We conjecture the additional hypothesis under which the same characterization is true in all dimensions. We give a partial answer to a question of S. Smale that in our context can be formulated as follows: can any polynomial automorphism of $C^k$ be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer?
On Commuting Polynomial Automorphisms of $mathbb{C}^k,$ $k ge 3.$
BISI, Cinzia
2008
Abstract
We characterize the polynomial automorphisms of $C^3,$ which commute with a regular automorphism. We use their meromorphic extension to $P^3$ and consider their dynamics on the hyperplane at infinity. We conjecture the additional hypothesis under which the same characterization is true in all dimensions. We give a partial answer to a question of S. Smale that in our context can be formulated as follows: can any polynomial automorphism of $C^k$ be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer?File in questo prodotto:
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