arXiv subjects

Álvaro Castañeda

Publications and source records attributed to Álvaro Castañeda.

22 records · Page 2Linked to original sources

arXiv2018

Smoothness of Topological Equivalence on the Half Line for Nonautonomous Systems

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 uniformly continuous homeomorphism inspired in the Palmer's one restricted to the positive half line, providing sufficient conditions ensuring its $C^{r}$--smoothness. Additionally, we study the preservation of the uniform stability properties by this homeomorphism.

math.CA↗

arXiv2018

A Spectral Dichotomy Version of the Nonautonomous Markus--Yamabe Conjecture

In this article we introduce a nonautonomous version of the Markus--Yamabe conjecture from an exponential dichotomy spectrum point of view. We prove the validity of this conjecture for the scalar and triangular case. Additionally we show that the origin is a global attractor for an autonomous system by using nonautonomous dynamical systems tools.

math.DS↗

arXiv2016

Injectivity and Almost Global Stability of Hurwitz Vector Fields

We present, in dimension $n \geq 3$, a survey of examples to: the Jacobian conjecture, the weak Markus--Yamabe conjecture. Furthermore, we show and construct new examples of vector fields where the origin is almost globally asymptotically stable by using the novel concept of density functions introduced by Rantzer.

math.DS↗

arXiv2012

The Discrete and Continuous Markus-Yamabe Stability Conjectures

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 number, I the identity map, and H a map with nilpotent Jacobian matrix JH. We consider the case where the rows of JH are linearly dependent over R and that where they are linearly independent over R. In the former, we find non-linearly triangularizable vector fields X for which the origin is a global attractor for both the continuous and the discrete dynamical systems generated by X. In the independent continuous case, we present a family of vector fields which have orbits escaping to infinity. In the independent discrete case, we present a large family of vector fields which have a periodic point of period 3.

math.DS↗