Brjuno conditions for linearization in presence of resonances

TL;DR

This paper offers a new proof for a holomorphic linearization theorem in the presence of resonances, utilizing a different arithmetic hypothesis and direct power series computations.

Contribution

It introduces a novel proof method for Rüssmann's linearization result, simplifying assumptions and employing direct power series calculations.

Findings

New proof under a more natural arithmetic hypothesis

Simplified proof technique using power series expansions

Extension of linearization results to resonant cases

Abstract

We present a new proof, under a slightly different (and more natural) arithmetic hypothesis, and using direct computations via power series expansions, of a holomorphic linearization result in presence of resonances originally proved by R\"ussmann.