Global stable manifolds in holomorphic dynamics under bunching conditions

TL;DR

This paper proves that under a weaker bunching condition, the stable manifolds of points in a hyperbolic set for a holomorphic automorphism are biholomorphic to complex vector spaces, extending classical linearization results.

Contribution

It introduces a weaker bunching condition ensuring stable manifolds are biholomorphic to complex vector spaces in holomorphic dynamics.

Findings

Stable manifolds are biholomorphic to complex vector spaces.

Weaker bunching condition than classical linearizability.

Extension of linearization results in holomorphic dynamics.

Abstract

We prove that the stable manifold of every point in a compact hyperbolic invariant set of a holomorphic automorphism of a complex manifold is biholomorphic to a complex vector space, provided that a bunching condition, which is weaker than the classical bunching condition for linearizability, holds.