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Smoothness of topological equivalence on the half line for nonautonomous systems

Part of: Topological dynamics Smooth dynamical systems: general theory Stability theory

Published online by Cambridge University Press:  07 May 2019

Álvaro Castañeda ,
Gonzalo Robledo  and
Pablo Monzón
Álvaro Castañeda
Affiliation:
Departamento de Matemáticas, Universidad de Chile, Casilla 653, Santiago, Chile (castaneda@uchile.cl; grobledo@uchile.cl)
Gonzalo Robledo
Affiliation:
Departamento de Matemáticas, Universidad de Chile, Casilla 653, Santiago, Chile (castaneda@uchile.cl; grobledo@uchile.cl)
Pablo Monzón
Affiliation:
Facultad de Ingeniería, Universidad de la República, Código Postal 11300, Montevideo, Uruguay (monzon@fing.edu.uy)
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Abstract

We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a homeomorphism inspired in the Palmer's one restricted to the positive half line, studying additional continuity properties and providing sufficient conditions ensuring its Cr–smoothness.

Keywords

topological equivalencenonautonomous differential equationsnonautonomous hyperbolicityuniform asymptotic stabilitydiffeomorphism

MSC classification

Primary: 34D09: Dichotomy, trichotomy
Secondary: 37C60: Nonautonomous smooth dynamical systems 37B25: Lyapunov functions and stability; attractors, repellers
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2484 - 2502
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Copyright
Copyright © Royal Society of Edinburgh 2019

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