Fiberwise Green functions of skew products semiconjugate to some polynomial products on C²

Abstract

We consider the dynamics of polynomial skew products that are semiconjugate to some polynomial products on C². We show that the fiberwise Green functions exist outside thin sets, whose upper semicontinuous regularizations are defined, continuous and plurisubharmonic on C². This result is obtained from the existence of Green functions of polynomials outside thin sets.