A generalized Grobman-Hartman theorem for nonautonomous dynamics

Abstract

The purpose of this note is to extend the recent generalized version of the Grobman-Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous to the nonautonomous dynamics. More precisely, we prove that any sufficiently small perturbation of a nonautonomous linear dynamics that admits a generalized exponential dichotomy is topologically conjugated to its linear part. In addition, we prove that under certain mild additional conditions, the conjugacy is in fact Hölder continuous.

V2: Added a missing argument in the proof of the main theorem. V3: Added example and strengthened Theorem 2. Final version

References in corpus (2)

• A generalized Grobman-Hartman theorem
• Generalized hyperbolicity for linear operators

Cited by in corpus (5)

• Linearization and H\" older Continuity for Nonautonomous Systems
• Smooth Linearization of Nonautonomous Coupled Systems
• On the linearization of infinite-dimensional random dynamical systems
• Multiscale linearization of nonautonomous systems
• Linearization and Hölder continuity of generalized ODEs with application to measure differential equations