Nonuniform contractions and density stability results via a smooth topological equivalence
Dynamical Systems
2018-08-24 v1
Abstract
We study the smoothness and preserving orientation properties of a global and nonautonomous version of the Hartman--Grobman Theorem when the linear system has a nonuniform contraction on the half line. The nonuniform contraction implies the existence of a density function (\emph{i.e} a dual type of Lyapunov function) for the linear system which combined with the above diffeomorphism allow us to construct a density function for the nonlinear system.
Keywords
Cite
@article{arxiv.1808.07568,
title = {Nonuniform contractions and density stability results via a smooth topological equivalence},
author = {Álvaro Castañeda and Pablo Monzón and Gonzalo Robledo},
journal= {arXiv preprint arXiv:1808.07568},
year = {2018}
}