We consider a nonautonomous system$\dot{x}=A(t)x+f(t,x,y),\dot{y}=g(t,y)$ and give conditions under which there is a transformation of the form $H(t,x,y)=(x+h(t,x,y),y)$ taking its solutions onto the solutions of the partially linearized system$\dot{x}=A(t)x,\dot{y}=g(t,y).$ Shi and Xiong [28] proved a special case where $g(t,y)$ was a linear function of y and $\dot{x}=A(t)x$ had an exponential dichotomy. Our assumptions on A and f are of the general form considered by Reinfelds and Steinberga [25], which include many of the generalizations of Palmer's theorem proved by other authors. Inspired by the work of Shi and Xiong, we also prove Hölder continuity of H and its inverse in x and y. Again the proofs are given in the context of Reinfelds and Steinberga but we show what the results reduce to when $\dot{x}=A(t)x$ is assumed to have an exponential dichotomy. The paper is concluded with the discrete version of the results.

我们考虑一个非自治系统$\dot{X}=\mathrm{一种}(吨)X+F(吨,X,是),\dot{是}=G(吨,是)$ 并给出形式发生转变的条件 $H(吨,X,是)=(X+H(吨,X,是),是)$ 将其解带到部分线性化系统的解上$\dot{X}=\mathrm{一种}(吨)X,\dot{是}=G(吨,是).$ Shi and Xiong [28] 证明了一个特例，其中 $G(吨,是)$是y的线性函数，并且$\dot{X}=\mathrm{一种}(吨)X$有指数二分法。我们对A和f 的假设是 Reinfelds 和 Steinberga [25] 考虑的一般形式，其中包括其他作者证明的 Palmer 定理的许多推广。受 Shi 和 Xiong 工作的启发，我们还证明了H及其在x和y 上的逆的Hölder 连续性。再次证明是在 Reinfelds 和 Steinberga 的上下文中给出的，但我们展示了结果减少到什么时候$\dot{X}=\mathrm{一种}(吨)X$假定具有指数二分法。论文以结果的离散版本结束。