A note on differentiability of the conjugacy in a delayed version of Hartman-Grobman Theorem-Reference-Cited by-同舟云学术

A note on differentiability of the conjugacy in a delayed version of Hartman-Grobman Theorem

Published:2022 Issue:12 Volume:27 Page:7591
ISSN:1531-3492
Container-title:Discrete and Continuous Dynamical Systems - B
language:
Short-container-title:DCDS-B

Author:

Gomez Adrian¹,Carrasco Dante¹,Elorreaga Heli¹

Affiliation:

1. Departamento de Matemática, Universidad del Bío-Bío, Concepción, 4051381, Chile

Abstract

<p style='text-indent:20px;'>In this work we study the differentiability properties of the conjugation in the Barreira-Valls version of the Hartman-Grobman Theorem for Non-autonomous and Delayed systems. Indeed, we show that the conjugacy in the Barreira-Valls Theorem is a <inline-formula><tex-math id="M1">\begin{document}$ C^1 $\end{document}</tex-math></inline-formula> diffeomorphism if we impose some extra hypothesis related with the decay of the perturbation.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Reference27 articles.

1. L. Barreira, C. Valls.Hyperbolicity via admissibility in delay equations, Indiana Univ. Math. J., 69 (2020), 1155-1179.

2. L. Barreira, C. Valls.Perturbations of delay equations, J. Differential Equations, 269 (2020), 7015-7041.

3. G. R. Belicki$\mathop {\rm{i}}\limits^ \vee $, Functional equations, and conjugacy of local diffeomorphisms of finite smoothness class, (Russian) Funkcional. Anal. i Priložen., 7 (1973), 17–28.

4. G. R. Belicki$\mathop {\rm{i}}\limits^ \vee $.Equivalence and normal forms of germs of smooth mappings (Russian), Uspekhi Math. Nauk, 33 (1978), 95-155.

5. Á. Castañeda, G. Robledo.Differentiability of Palmer's linearization theorem and converse result for density functions, J. Differential Equations, 259 (2015), 4634-4650.

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