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

Pages: 985 - 996, Volume 31, Issue 3, November 2011

doi:10.3934/dcds.2011.31.985       Abstract        References        Full Text (355.2K)       Related Articles

Kohei Ueno - Toba National College of Maritime Technology, Mie 517-8501, Japan (email)

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.

Keywords:  Complex dynamics, skew product, Green function.
Mathematics Subject Classification:  Primary: 32H50; Secondary: 30D05, 37H99.

Received: June 2010;      Revised: February 2011;      Published: August 2011.

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