Backward iteration in strongly convex domains

2011/04/28 by Marco Abate, Abate, Marco, Jasmin Raissy +1
Mathematics · #32H50 #37F99 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1104.5370

openalex publication_date 2011/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a backward orbit with bounded Kobayashi step for a hyperbolic or strongly elliptic holomorphic self-map of a bounded strongly convex domain in the d-dimensional complex Euclidean space necessarily converges to a boundary fixed point, generalizing previous results obtained by Poggi-Corradini in the unit disk and by Ostapyuk in the unit ball.

Related

• Backward iteration in the unit ball
• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• Backward orbits in the unit ball
• Canonical models for the forward and backward iteration of holomorphic maps
• Common boundary regular fixed points for holomorphic semigroups in strongly convex domains