On the Siegel-Sternberg linearization theorem. (English) Zbl 1482.46047
Summary: 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.
MSC:
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
| 26E10 | \(C^\infty\)-functions, quasi-analytic functions |
| 37C10 | Dynamics induced by flows and semiflows |
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