English

Linearization of a nonautonomous unbounded system with nonuniform contraction: A Spectral Approach

Classical Analysis and ODEs 2020-01-13 v2

Abstract

For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of homeomorphisms. The first one is set up by considering the fact that linear system is almost reducible to diagonal system with a small enough perturbation where the diagonal entries belong to spectrum of the nonuniform exponential dichotomy; and the second one is constructed in terms of the crossing times with respect to unit sphere of an adequate Lyapunov function associated to the linear system.

Keywords

Cite

@article{arxiv.1905.07319,
  title  = {Linearization of a nonautonomous unbounded system with nonuniform contraction: A Spectral Approach},
  author = {I. Huerta},
  journal= {arXiv preprint arXiv:1905.07319},
  year   = {2020}
}