نتایج جستجو برای: grobman theorem

تعداد نتایج: 144113  

2008
BORIS HASSELBLATT Philip Hartman

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))...

Journal: :Proceedings of the American Mathematical Society 2020

Journal: :Int. J. Systems Science 2004
Wassim M. Haddad Sergey G. Nersesov VijaySekhar Chellaboina

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...

Journal: :Journal of Applied Analysis and Computation 2022

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...

Journal: :Journal of Differential Equations 1986

Journal: :Collectanea Mathematica 2021

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...

Journal: :Journal of Dynamics and Differential Equations 2006

Journal: :Anais da Academia Brasileira de Ciências 2015

Journal: :international journal of nonlinear analysis and applications 0
khosro sayevand faculty of mathematical sciences, malayer university, p.o.box 16846-13114, malayer, iran

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

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