H(?)lder Regularity Of Grobman-Hartman Theorem For Dynamic Equations On Measure Chains

In 1990, Hilger first introduced the concept of measure chains in《Result Math.》 Recently, there are some papers considering linearization problems on measure chains([2], [37]). However, there is no paper discussing the H(?)lder regularity of the transformation H(t, x). This paper fill the gap. We establish a strict proof of the H(?)lder regularity of the transformation H(t,x). We·show that the conjugating function H(t,x) in the generlized Hartman-Grobman theorem is always H(?)lder continuous. This paper is organized as follows:In chapter 1, we briefly introduce the research background and some lemmas of this dissertation.In chapter 2, we introduce some notations and basic terminology for the calculus on measure chains. Then we also introduced definition of exponential dichotomy and Bellman inequality on measure chains.In chapter 3, we state our main result:There exists a one-to-one correspondence H(t,x) between solutions of the linear system and the nonlinear system; The conju-gating function H(t,x) satisfies:||H(t,x) - H(t,(?))||±to,c,d≤p||x-(?)||q;also the inverse H-1(t, x):= G(t, x) satisfies:||G(t, y)-G(t,(?))||±to,c,d≤(?)||y-(?)||(?);In chapter 4, the main result is proved.