5 papers
Nonautonomous Linear Systems: Exponential Dichotomy and its Applications
Ãlvaro Castañeda, Gonzalo Robledo
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential d…
Generalized Evolution Semigroups and Dichotomies for Evolution Families on Banach Spaces
Ãlvaro Castañeda, Verónica Poblete, Gonzalo Robledo
This paper develops a comprehensive theory generalizing exponential decay patterns for evolution processes in Banach spaces. We replace classical exponential bounds with more flexi…
Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via -Dichotomies
Ãlvaro Castañeda, Heli Elorreaga
We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $Î…
Smoothness of linearization by mixing parameters of dichotomy, bounded growth and perturbation
Ãlvaro Castañeda, Ignacio Huerta, Gonzalo Robledo
We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonunifo…
An application of a nonuniform global stability problem to the study of parametrized polynomial automorphisms
Ãlvaro Castañeda, Ignacio Huerta, Gonzalo Robledo
We propose a handful of definitions of injectivity for a parametrized family of maps and study its link with a global nonuniform stability conjecture for nonautonomous differential…