On linearization of biholomorphism with non-semi-simple linear part at a fixed point

TL;DR

This paper establishes conditions under which biholomorphic germs with non-semi-simple linear parts at a fixed point can be holomorphically linearized, extending classical results to more complex eigenvalue configurations.

Contribution

It introduces new Diophantine-like conditions for linearization of germs with nontrivial Jordan blocks, broadening the scope of classical linearization theorems.

Findings

Proves holomorphic linearizability under specified eigenvalue conditions.

Extends classical linearization results to non-semi-simple cases.

Introduces new Diophantine-like conditions related to quasi-resonance.

Abstract

We prove the holomorphic linearizability of germs of biholomorphisms of (C n , 0), fixing the origin, point at which the linear part has nontrivial Jordan blocks under the following assumptions : We first assume the eigenvalues are of modulus less or equal than 1, and that they are non-resonant. We also assume that they satisfied not only a classical Diophantine condition but also new Diophantine-like conditions related to quasi-resonance phenomena.