We establish a general version of the Siegel-Sternberg linearization theorem for ultradiffentiable maps which includes the analytic case, the smooth case and the Gevrey case. It may be regarded as a small divisior theorem without small divisor conditions. Along the way we give an exact characterization of those classes of ultradifferentiable maps which are closed under composition, and reprove regularity results for solutions of ode’s and pde’s.

中文翻译：

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关于Siegel-Sternberg线性化定理

我们为超微分图建立了Siegel-Sternberg线性化定理的通用版本，其中包括解析案例，光滑案例和Gevrey案例。可以将其视为没有小除数条件的小除数定理。在此过程中，我们给出了在组成下封闭的那些超微分图类的精确刻画，并证明了ode和pde的解的正则性结果。