Equivalence of stability properties for ultradifferentiable function classes

TL;DR

This paper establishes that various stability properties such as composition, inversion, and solving differential equations are all equivalent within ultradifferentiable function classes, providing a unified understanding of their behavior.

Contribution

It proves the equivalence of multiple stability properties in ultradifferentiable classes, offering a comprehensive characterization of their stability features.

Findings

Stability under composition, inversion, and ODE solutions are equivalent.

Ultradifferentiable classes exhibit unified stability properties.

The results unify understanding of ultradifferentiable function behaviors.

Abstract

We characterize stability under composition, inversion, and solution of ordinary differential equations for ultradifferentiable classes, and prove that all these stability properties are equivalent.