Smooth Linearization of Nonautonomous Differential Equations with a Nonuniform Dichotomy

Abstract

In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its spectrum and then give a spectral bound condition for the linearization of such equations to be simultaneously differentiable at 0 and Hölder continuous near 0. Restricted in the autonomous case, our result is the first one that gives a rigorous proof for simultaneously differentiable and Hölder linearization of hyperbolic systems without any non-resonant conditions.

arXiv commentFinal version incorporating comments from the referees. Accepted for publication in Proceedings of the London Mathematical Society

References in corpus (2)

• Differentiability of Palmer's linearization Theorem and converse result for density functions
• Nonuniform contractions and density stability results via a smooth topological equivalence

Cited by in corpus (6)

• Linearization and H\" older Continuity for Nonautonomous Systems
• Quasi-shadowing for partially hyperbolic dynamics on Banach spaces
• A generalized Grobman-Hartman theorem for nonautonomous dynamics
• Generalized dichotomies via time rescaling
• Multiscale linearization of nonautonomous systems
• Linearization and Hölder continuity of generalized ODEs with application to measure differential equations