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Smooth moduli-free normal forms of hyperbolic germs of diffeomorphisms
Authors:Zhihua Ren  Zhaoxia Peng
Affiliation:1. College of Applied Sciences , Beijing University of Technology , Beijing , China;2. LAGIS , UMR 8219 CNRS, Ecole Centrale de Lille, Villeneuve d’Ascq , 59651 , France
Abstract:In this paper, we study the smooth classifications of germs of diffeomorphisms near a hyperbolic fixed point based on the smooth moduli-free polynomial normal forms of the corresponding diffeomorphisms and give the following result. On  /></span>, <i>n</i> ≤ 5, with two kinds of exceptions, any two hyperbolic germs of diffeomorphisms with generic nonlinear parts are at least <i>C</i> <sup>1</sup> conjugated if and only if their linear parts are similar.</td>
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Keywords:smooth conjugacy  moduli-free normal form  hyperbolic fixed point
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