English

On the Siegel-Sternberg linearization theorem

Dynamical Systems 2017-04-06 v2 Classical Analysis and ODEs

Abstract

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 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. This will open up new directions in \textsc{kam}-theory and other applications of ultradifferentiable functions.

Keywords

Cite

@article{arxiv.1702.03691,
  title  = {On the Siegel-Sternberg linearization theorem},
  author = {Jürgen Pöschel},
  journal= {arXiv preprint arXiv:1702.03691},
  year   = {2017}
}

Comments

34 pages

R2 v1 2026-06-22T18:16:34.664Z