| 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. |
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