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arXiv · 2409.19197

Smoothness of linearization by mixing parameters of dichotomy, bounded growth and perturbation

Álvaro Castañeda·Ignacio Huerta·Gonzalo Robledo
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Abstract

We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and nonuniform bounded growth property. Additionally, the quasilinear perturbation is dominated by an increasing exponential function. Emphasis is placed on employing a set of parameters to describe the conditions of dichotomy, bounded growth and quasilinear perturbations. Finally, we prove that modifying these conditions enables us to achieve a broader smoothness interval.

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Álvaro Castañeda, Ignacio Huerta, Gonzalo Robledo. 2024-09-28. Smoothness of linearization by mixing parameters of dichotomy, bounded growth and perturbation. https://arxiv.org/abs/2409.19197

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