On Holder Dependence of the Parameterized Hartman–Grobman Theorem  

作　　者：Wen Meng ZHANG Peng LIU Xuan LEI 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第1期137-147,共11页数学学报（英文版）

基　　金：supported by NSFC(Grant No.11671061);NSF-CQ(Grant No.cstc2018kjcxljrc0049);supported by NSF-CQ(Grant No.cstc2018jcyj AX0418)。

摘　　要：The well-known Hartman-Grobman Theorem says that a C~1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphismΦ.For parameterized systems F_(θ),known results show that the corresponding homeomorphismsΦ_(θ)exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameterθ.In this paper,we further extend the results to Holder dependence ofΦ_(θ)onθby Pugh's strategy,but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of F_(θ).This requires a new Holder linearization result for every F_(θ).

关 键 词：Holder linearization dependence on parameter HYPERBOLICITY 

分 类 号：O186.1[理学—数学]