A Grobman-Hartman theorem for a differential equation with piecewise constant generalized argument

向量丛上Hartman-Grobman定理的Hölder正则性

Holder regularity of Hartman-Grobman theorem on vector bundle

本文研究向量丛上Hartman-Grobman定理的Hölder正则性，构造等价连续丛范数与合适截断函数，完成相关正则性论证。

Higher regularity of homeomorphisms in the Hartman-Grobman theorem for semilinear evolution equations

Hein and Prüss [J. Differential Equations, 261(2016)4709-4727] presented a version of Hartman-Grobman type $C^{0}$ linearization result for semilinear hyperbolic evolution equations. They showed that the linearising map (homomorphism) and its inverse are Hölder continuous. An important question: is it possible to improve the regularity of the homomorphisms? In the present paper, we prove that if the mild solutions of semilinear system are bounded, then the regularity of the homomorphisms is Lipchitzian, but the inverse is merely Hölder continuous. We also give a generalized local linearization…

Higher regularity of homeomorphisms in the Hartman-Grobman theorem and a conjecture on its sharpness

Hartman-Grobman theorem states that there is a homeomorphism H sending the solutions of the nonlinear system onto those of its linearization under suitable assumptions. Many mathematicians have made contributions to prove Hölder continuity of the homeomorphisms. However, is it possible to improve the Hölder continuity to Lipschitzian continuity? This paper gives a positive answer. We formulate the first result that the homeomorphism is Lipschitzian, but not $C^1$, while its inverse is merely Hölder continuous, but not Lipschitzian. It is interesting that the regularity of the homeomorphism is …

通过μ-二分性得到的延迟非自治Hartman–Grobman定理中共轭的$C^{1}$光滑性

$C^{1}$ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via $μ$-Dichotomies

本文研究有限延迟非自治系统中线性部分满足μ-二分性时Hartman–Grobman定理的共轭可微性，证明在适当非线性扰动条件下该共轭为$C^{1}$微分同胚。

代数二分法的Hartman-Grobman定理

A Hartman-Grobman theorem for algebraic dichotomies

本文针对代数二分法这一指数二分法的推广概念，提出了相应的Hartman-Grobman线性化定理，推广了Palmer定理，证明了线性化同胚的Hölder连续逆性质，并对比了两类二分法的积分估计差异。

Banach 丛上的 Hartman-Grobman 定理

A Hartman-Grobman theorem on Banach bundles

本文在 Banach 丛上建立广义 Hartman-Grobman 线性化定理，统一处理各类二分性，并推广到控制仿射系统。