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.
Abate, M., Bracci, F. (2016). Common Boundary Regular Fixed Points for Holomorphic Semigroups in Strongly Convex Domains. In B.U. Mark L. Agranovsky (a cura di), Complex Analysis and Dynamical Systems VI: Part 2: Complex Analysis, Quasiconformal Mappings, Complex Dynamics (pp. 1-14). PROVIDENCE, USA : AMER MATHEMATICAL SOC [10.1090/conm/667/13527].
Common Boundary Regular Fixed Points for Holomorphic Semigroups in Strongly Convex Domains
Bracci, Filippo
2016-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
