2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65846The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in ${\Bbb C}^n$ under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in ${\Bbb C}^n$ does not exceed $n$.14 pagesComplex Variables32M05text