The Hartman–Grobman Theorem (see [3, page 353]) was proved by Philip Hartman in 1960 [5]. It had been announced byGrobman in 1959 [1], likely unbeknownst to Hartman, and Grobmanpublished his proof in 1962 [2], likely without knowing of Hartman’s work. (Grobman attributes the question to Nemycki and an earlier partial result to R.M. Minc (citing Nauč. Dokl. Vysš. Školy. Fiz.-Mat. Nauki 1 (1958))...

Algebraic dichotomy is a generalization of an exponential (see Lin[?]). This paper gives version Hartman-Grobman linearization theorem assuming that linear system admits algebraic dichotomy, which generalizes the Palmer's theorem. Besides, we prove homeomorphism in Hölder continuous (and has inverse). Comparing with more complicate. The leads us to estimates $\int_{-\infty}^{t}e^{-\alpha(t...

One of the most fundamental results in analysing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincaré’s theorem. The proof of this result involves system analytic arguments along with the Hartman–Grobman theorem. Using the notions of stability of sets, lower semicontinuous Lyapunov functions are constructed to provide a Lyapunov function proof of Poincar...

In this paper we give the main ideas to show that a real analytic vector field in R3 with a singular point at the origin is locally topologically equivalent to its principal part defined through Newton polyhedra under non-degeneracy conditions.

The purpose of this note is to extend the recent generalized version Grobman-Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous nonautonomous dynamics. More precisely, we prove that any sufficiently small perturbation a linear dynamics admits exponential dichotomy topologically conjugated its part. In addition, under certain mild additional conditions, conjugacy in fa...