A Wong-Rosay type theorem for proper holomorphic self-maps

TL;DR

This paper proves that proper holomorphic self-maps of certain bounded domains in complex space are automorphisms of the ball if their dynamics approach a strictly pseudoconvex boundary point, extending Wong-Rosay results.

Contribution

It establishes a Wong-Rosay type theorem for sequences of proper holomorphic self-maps with unbounded degrees, characterizing when such maps are automorphisms.

Findings

Proper holomorphic self-maps with boundary dynamics approaching a strictly pseudoconvex point are automorphisms.

The result applies to sequences of maps with unbounded degrees.

The theorem extends classical Wong-Rosay results to new settings.

Abstract

We show that the only proper-holomorphic self-maps of bounded domains in C^k whose dynamics escape to a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type result for a sequence of maps whose degrees are a priori unbounded.