文档介绍：-Holder linearizationVictoria RayskinUniversity of Texas, AustinDepartment of MathematicsAustin, TX 78703E-mail: ******@ well known theorem of Hartman-Grobman says that a C2dif-feomorphism f : Rn !Rn with a hyperbolic xed point at 0 can betopologically conjugated to the linear di eomorphism L = df(0) (ina neighborhood of 0). On the other hand, if a non-planar map hasresonance, then linearization may not be C1. A counter-example isdue to P. Hartman (see H2]). In this paper we will show that for any2(0;1) there exists an -Holder linearization in a neighborhood of0 for the counter-example of Hartman. No resonance condition willbe required. A linearization of a more general map will be IntroductionLet f be a C3di eomorphism with a hyperbolic xed point at 0 and linearpart L. We will say that f can be linearized if there exist a neighborhood Uof 0 and homeomorphism h : U ! h(U) with h(0) = 0 such that h f = L hon well known theorem of Hartman-Grobman says that such a di eomor-phism can be topologically linearized (locally). See H1]. A simpler proofcan be found in P].However, if linearization is only C0, it is inconvenient for various appli-cations. Of course, if we will make additional assumptions on resonance, wewill obtain smooth linearization. (See S]). But this technical assumption isunnatural for . Hartman showed ( ?]) that in the planar case, a C2di eomorphismwith a hyperbolic xed point can be . Belitskii and S. van Strien ( B], ABZ], v-S]) have considered thisproblem in higher dimensions and proved that for some less then 1 thereexists a local linearization in the -Holder class. In their works this dependon the 's counter-example ( H2]) shows that a non-planar map may notbe C1linearizable, and bounds the search for this paper, rst, we will show that for any 2 (0;1) there existsan -Holder linearization of the Hartman map in a neighborhood of 0. Noresonance conditi