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Attracting basins for automorphisms of $\bbfC^2$. (English) Zbl 0932.37028
The paper deals with the interesting question whether an automorphism of $\bbfC^n$ tangent to the identity can have a domain of attraction, and if so, whether that domain is biholomorphic to $\bbfC^n$. It is obvious that this cannot happen when $n=1$, due to the fact that the automorphism group of $\bbfC$ is the group of affine mappings $z\mapsto az+b$, $a\ne 0$. The main result of the paper states that there exist an automorphism $\bbfC^2$ tangent to the identity with an invariant domain of attraction to the origin, biholomorphic to $\bbfC^2$, on which the automorphism is biholomorphic conjugate to the map $(x,y)\mapsto(x-1,y)$.

37F10Polynomials; rational maps; entire and meromorphic functions
37F15Expanding maps; hyperbolicity; structural stability
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