On the domains with noncompact automorphism groups

For automorphism groups, we prove that the orbit accumulation points are either hyperbolic or parabolic. This answers the question pertaining to the non-compactness of the inverses of a non-compact sequence of automorphisms. We also partially extend a previous theorem of the author on global pseudoconvexity to higher dimensions, provided it admits a non-compact automorphism group. In general, a full extension does not exist. We provide an example to elaborate on the nonexistence. This example is carefully constructed and an exact sequence of automorphisms is explicitly found.