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 Volume 1, Number 1, 2011, Pages 1-8                                                                DOI：10.11948/2011001 Analytic Conjugation, Global Attractor, and the Jacobian Bo Deng Keywords:Jacobian Conjecture, Analytic Conjugation, Global Stability, Polynomial Automorphism, Jacobian Polynomial, Analytic Linearization. Abstract: It is proved that the dilation $\lambda f$ of an analytic map $f$ on ${\bf C}^n$ with $f(0)=0,f'(0)=I, |\lambda|>1$ has an analytic conjugation to its linear part $\lambda x$ if and only if $f$ is an analytic automorphism on ${\bf C}^n$ and $x=0$ is a global attractor for the inverse $(\lambda f)^{-1}$. This result is used to show that the dilation of the Jacobian polynomial of [12] is analyticly conjugate to its linear part. PDF      Download reader