39 citations · 45 across the 9 of their papers we have counts for
17 papers
A family of Hurwitz polynomial vector fields in having non-constant periodic orbits
Álvaro Castañeda, Salomón Rebollo-Perdomo
We construct a two-parameter family of polynomial vector fields in and prove that, on a nonempty open set of parameter values, every member of the family is Hurwitz…
The weak Markus--Yamabe conjecture fails in dimension 14
Álvaro Castañeda, Gerardo Honorato, Francisco Valenzuela-Henríquez
We show that the weak Markus--Yamabe conjecture fails in every dimension . We first prove a chain realization theorem: every polynomial Keller map $F=\I+H$ of with…
A generalization of Siegmund's normal forms theorem to systems with -dichotomies
Álvaro Castañeda, Néstor Jara
We establish a theorem concerning the normal forms by examining the newly presented concept of -dichotomy. This work establishes the nonresonance condition based on the associat…
The dichotomy spectrum approach for a global nonuniform asymptotic stability problem: Triangular case via uniformization
Álvaro Castañeda, Ignacio Huerta, Gonzalo Robledo
By considering the nonuniform exponential dichotomy spectrum, we introduce a global asymptotic nonuniform stability conjecture for nonautonomous differential systems, whose restric…
Discrete and continuous dynamics of real -dimensional nilpotent polynomial vector fields
Álvaro Castañeda, Salomón Rebollo-Perdomo
A large class of real -dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete an…
An application of a nonuniform global stability problem to the study of parametrized polynomial automorphisms
Álvaro 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…
Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line
Álvaro Castañeda, Pablo González, Gonzalo Robledo
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the…
Nilpotent Jacobians and Almost Global Stability
Álvaro Castañeda, Maximiliano Machado-Higuera
In this article we study maps with nilpotent Jacobian in distinguishing the cases when the rows of are linearly dependent over and when they are li…
Nonuniform contractions and density stability results via a smooth topological equivalence
Álvaro Castañeda, Pablo Monzón, Gonzalo Robledo
We study the smoothness and preserving orientation properties of a global and nonautonomous version of the Hartman--Grobman Theorem when the linear system has a nonuniform contract…
A new class of Nilpotent Jacobians in any dimension
Álvaro Castañeda, Arno van den Essen
The classification of the nilpotent Jacobians with some structure has been an object of study because of its relationship with the Jacobian Conjecture. In this paper we classify th…
Smoothness of Topological Equivalence on the Half Line for Nonautonomous Systems
Álvaro Castañeda, Pablo Monzón, Gonzalo Robledo
We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable…
Nonuniform Almost Reducibility of Nonautonomous Linear Differential Equations
Álvaro Castañeda, Ignacio Huerta
We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be expressed as diagonal system with a perturbation which is small enoug…
Almost reducibility of linear difference systems from a spectral point of view
Alvaro Castañeda, Gonzalo Robledo
We prove that, under some conditions, a linear nonautonomous difference system is Bylov's almost reducible to a diagonal one whose terms are contained in the Sacker and Sell spectr…
Injectivity and Almost Global Stability of Hurwitz Vector Fields
Álvaro Castañeda, Víctor Guíñez
We present, in dimension , a survey of examples to: the Jacobian conjecture, the weak Markus--Yamabe conjecture. Furthermore, we show and construct new examples of vector…
A topological equivalence result for a family of nonlinear difference systems having generalized exponential dichotomy
Alvaro Castañeda, Gonzalo Robledo
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotom…
Differentiability of Palmer's linearization Theorem and converse result for density functions
Alvaro Castañeda, Gonzalo Robledo
We study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism between the solutions of a line…
The Discrete and Continuous Markus-Yamabe Stability Conjectures
Álvaro Castañeda, Víctor Guíñez
We study the discrete and continuous versions of the Markus- Yamabe Conjecture for polynomial vector fields in R^n (especially when n = 3) of the form X = λI+H where λis a real num…