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

Kohei Ueno

doi:10.3934/dcds.2014.34.2283

Article Contents

2014, Volume 34, Issue 5: 2283-2305. Doi: 10.3934/dcds.2014.34.2283

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

Kohei Ueno^1,

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

Received: November 30, 2012

Revised: July 31, 2013

Published: April 2014

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Abstract

We study the dynamics of polynomial skew products on $\mathbb{C}^2$. By using suitable weights, we prove the existence of several types of Green functions. Largely, continuity and plurisubharmonicity follow. Moreover, it relates to the dynamics of the rational extensions to weighted projective spaces.

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

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