Linearization and Hölder continuity for nonautonomous systems

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