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We study the dynamics of a superattracting skew product $f$ on the attractingbasin. As the first strategy, we find out forward $f$-invariant wedge-shapedregions in the basin, on some of which $f$ is conjugate to monomial maps, andconsider whether the unions of all the preimages of the regions coincide withthe basin. As the second strategy, we show the existence and properties ofseveral kinds of plurisubharmonic functions of $f$, the main functions of whichare induced from the B\"{o}ttcher coordinates, and investigate the asymptoticbehavior of the functions toward the boundaries of the unions. Consequently, weobtain a plurisubharmonic function on the complement of specific fibers in thebasin, which is continuous and pluriharmonic on open and dense subsets of thecomplement and describes an certain weighted vertical dynamics well.

Dynamics of superattracting skew products on the attracting basins: B\"{o}ttcher coordinates and plurisubharmonic functions