Let D be a bounded strongly convex domain with smooth boundary in C^N . Let F_t be a continuous semigroup of holomorphic self-maps of D. We prove that if p ∈ ∂D is an isolated boundary regular fixed point for F_{t_0} for some t_0 > 0, then p is a boundary regular fixed point for F_t for all t ≥ 0. Along the way we also study backward iteration sequences for elliptic holomorphic self-maps of D.
Common boundary regular fixed points for holomorphic semigroups in strongly convex domains
ABATE, MARCO;
2016-01-01
Abstract
Let D be a bounded strongly convex domain with smooth boundary in C^N . Let F_t be a continuous semigroup of holomorphic self-maps of D. We prove that if p ∈ ∂D is an isolated boundary regular fixed point for F_{t_0} for some t_0 > 0, then p is a boundary regular fixed point for F_t for all t ≥ 0. Along the way we also study backward iteration sequences for elliptic holomorphic self-maps of D.File in questo prodotto:
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