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首页> 外文期刊>Journal of Differential Equations >Sharpness for C-1 linearization of planar hyperbolic diffeomorphisms
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Sharpness for C-1 linearization of planar hyperbolic diffeomorphisms

机译：平面双曲微分C-1线性化的清晰度

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摘要

C-1 linearization preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions. Planar hyperbolic diffeomorphisms are the most elementary ones of representatively technical difficulties in the study of C-1 linearization. In the Poincare domain (both eigenvalues inside the unit circle S-1) a lower bound alpha(0) was given such that C-1,C-alpha smoothness with alpha(0) < alpha <= 1 admits C-1 linearization. Our first purpose of this paper is to prove the sharpness of cep and give a weaker linearization for a < cep. In the Siegel domain (one eigenvalue inside S-1 but the other outside S-1) it is known that C-1,C-alpha smoothness admits C-1 linearization for all alpha is an element of (0,1]. The second purpose is to prove that the C-1 linearization is actually a C-1,C-beta linearization and give sharp estimates for beta. (C) 2014 Elsevier Inc. All rights reserved.
机译：C-1线性化保留了平滑的动力学行为，并在特征方向上区分了定性性质。在C-1线性化研究中，代表性的技术难题是平面双曲型微分的最基本形式。在Poincare域中（两个特征值均在单位圆S-1内）给出了下限alpha（0），使得alpha（0）

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