Backward iteration in strongly convex domains

TL;DR

This paper proves that backward orbits with bounded Kobayashi step in strongly convex domains always converge to boundary fixed points, extending known results from the unit disk and ball to higher dimensions.

Contribution

It generalizes previous convergence results for backward orbits to bounded strongly convex domains in higher-dimensional complex spaces.

Findings

Backward orbits with bounded Kobayashi step converge to boundary fixed points.

The result extends prior work from the unit disk and ball to strongly convex domains.

Convergence holds for hyperbolic or strongly elliptic holomorphic self-maps.

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.