Weighted Green functions of nondegenerate polynomial skew products on $\mathbb{C}^2$

Kohei Ueno

doi:10.3934/dcds.2011.31.985

Article Contents

2011, Volume 31, Issue 3: 985-996. Doi: 10.3934/dcds.2011.31.985

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Weighted Green functions of nondegenerate polynomial skew products on $\mathbb{C}^2$

Kohei Ueno^1,

1.
Toba National College of Maritime Technology, Mie 517-8501

Received: May 31, 2010

Revised: January 31, 2011

Published: August 2011

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Abstract

We consider the dynamics of nondegenerate polynomial skew products on $\mathbb{C}^{2}$. The paper includes investigations of the existence of the Green and fiberwise Green functions of the maps, which induce generalized Green functions that are well-behaved on $\mathbb{C}^{2}$, and examples of the Green functions which are not defined on some curves in $\mathbb{C}^{2}$. Moreover, we consider the dynamics of the extensions of the maps to holomorphic or rational maps on weighted projective spaces.

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Mathematics Subject Classification: Primary: 32H50; Secondary: 30D05, 37H99.

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