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

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


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