Differentiability of Palmer's linearization Theorem and converse result for density functions

Abstract

We study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism $H$ between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that $H$ is a $C^2$ preserving orientation diffeomorphism are given. As an application, we generalize a converse result of density functions for a nonlinear system in the nonautonomous case.

Cited by in corpus (11)

• Smooth Linearization of Nonautonomous Differential Equations with a Nonuniform Dichotomy
• Linearization and H\" older Continuity for Nonautonomous Systems
• A generalized Grobman-Hartman theorem for nonautonomous dynamics
• Smooth Linearization of Nonautonomous Coupled Systems
• Nonuniform contractions and density stability results via a smooth topological equivalence
• Multiscale linearization of nonautonomous systems
• A note on the differentiability of Palmer's topological equivalence for discrete systems
• Stability and Instability Divergence Conditions for Dynamical Systems
• Divergence Conditions for Investigation and Control of Nonautonomous Dynamical Systems
• Linearization and Hölder continuity of generalized ODEs with application to measure differential equations
• General divergent stability conditions of dynamic systems