论文标题
非自主系统的线性化和H \'较旧的连续性
Linearization and H\" older Continuity for Nonautonomous Systems
论文作者
论文摘要
我们考虑一个非自主系统\ [\ dot x = a（t）x+f（t，x，y），\ quad \ dot y = g（t，y）\]，并给出$ h（t，x，y）=（x+h（x+h（x+h（t，x，y），y），将其求解）的转换的条件，将其求解为unlute untion for n ofters Syste x = a（t）x，\ quad \ dot y = g（t，y）。我们对$ A $和$ f $的假设是Reinfelds和Steinberga \ Cite {RS}所考虑的一般表格，其中包括其他作者证明的Palmer定理的许多概括。受Shi和Xiong的工作的启发，我们还证明了“ $ H $的较旧连续性及其在$ x $和$ y $中的倒数。再次在Reinfelds和Steinberga的背景下给出了证据，但我们将结果显示到$ \ dot x = a（t）x $的何时降低了dichote dichoteption。
We consider a nonautonomous system \[ \dot x=A(t)x+f(t,x,y),\quad \dot y = g(t,y)\] 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 \[ \dot x=A(t)x,\quad \dot y = g(t,y).\] Shi and Xiong \cite{SX} 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 \cite{RS}, 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 H\" older 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.
