Smooth linearization of nonautonomous differential equations with a nonuniform dichotomy

By D. Dragičević, Weinian Zhang, Wenmeng Zhang. Proceedings of the London Mathematical Society, 2017

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In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of a 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 to 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 nonresonant conditions.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

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