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arXiv · 1808.07568

Nonuniform contractions and density stability results via a smooth topological equivalence

Álvaro Castañeda·Pablo Monzón·Gonzalo Robledo
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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.

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Álvaro Castañeda, Pablo Monzón, Gonzalo Robledo. 2018-08-22. Nonuniform contractions and density stability results via a smooth topological equivalence. https://arxiv.org/abs/1808.07568

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