Normal forms of hyperbolic logarithmic transseries

TL;DR

This paper determines the normal forms of hyperbolic logarithmic transseries under specific transformations, providing conditions for linearization, and develops an algorithmic approach using fixed point theorems and Picard sequences.

Contribution

It introduces a complete characterization of normal forms for hyperbolic logarithmic transseries and offers an explicit, algorithmic method for normalization.

Findings

Normal forms characterized for hyperbolic logarithmic transseries

Conditions established for when the normal form is linear

An algorithmic normalization procedure using fixed point theorems

Abstract

We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.