English

Hyperbolicity and Averaging for the Srzednicki-W\'ojcik equation

Classical Analysis and ODEs 2016-07-12 v1

Abstract

For the Srzednicki-W\'ojcik equation, the planar nonautonomous ODE parameterized by κR\kappa \in \mathbb{R}, z=z(1+z2exp(iκt)),z(t)C z'=\overline{z}(1+ |z|^2 \exp(i \kappa t)), \qquad z(t) \in \mathbb{C} using averaging we show how the region of hyperbolicty grows with κ|\kappa|. Based on this we give bounds on the sizes of bounded orbits.

Keywords

Cite

@article{arxiv.1607.02611,
  title  = {Hyperbolicity and Averaging for the Srzednicki-W\'ojcik equation},
  author = {Piotr Zgliczyński},
  journal= {arXiv preprint arXiv:1607.02611},
  year   = {2016}
}