Common Boundary Regular Fixed Points for Holomorphic Semigroups in Strongly Convex Domains

Let D be a bounded strongly convex domain with smooth boundary in C-N. Let (phi(t)) be a continuous semigroup of holomorphic self-maps of D. We prove that if p is an element of partial derivative D is an isolated boundary regular fixed point for phi(t0) for some t(0) > 0, then p is a boundary regular fixed point for phi(t) for all t >= 0. Along the way we also study backward iteration sequences for elliptic holomorphic self-maps of D.