Neptalí Romero | Universidad Centroccidental Lisandro Alvarado (original) (raw)

Papers by Neptalí Romero

Revista De La Union Matematica Argentina, May 23, 2022

We provide sufficient conditions in order to show that the image set of a continuous and shift-co... more We provide sufficient conditions in order to show that the image set of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space. Additionally, if such a map is injective, then its inverse is also continuous and shift-commuting.

espanolEl objetivo de estas notas es clasificar por clases de conjugacion la coleccion de r-autom... more espanolEl objetivo de estas notas es clasificar por clases de conjugacion la coleccion de r-automatas celulares generada por las permutaciones de r reglas locales fijadas. EnglishThe main goal of this note is to class i fy by conjugacy classes the collect i on of r-cellular automata generated by the permutations of r fixed local rules.

Journal of Mathematical Analysis and Applications, 2017

In this article we consider Lyapunov stability of orbits of self-maps on metric spaces. The main ... more In this article we consider Lyapunov stability of orbits of self-maps on metric spaces. The main interest is posed on the relationship between past stability and expansiveness. It is shown that an expansive map with past stable orbits must be expanding. Moreover, when there are not past stable orbits, then every point has a future stable set of large diameter.

Applied Mathematics Letters, 2006

The main goal of this work is to show an extension of well known Hedlund's theorem which states t... more The main goal of this work is to show an extension of well known Hedlund's theorem which states that in the Cantor topology the cellular automata are the continuous shift preserving maps. This extension maintains the topological structure and uses the concept of barriers of Set Theory to generalize the notion of local rule in the definition of cellular automata.

Journal of Mathematical Analysis and Applications, 2014

ABSTRACT In this paper, a class of diffusive coupled logistic map with large strength is consider... more ABSTRACT In this paper, a class of diffusive coupled logistic map with large strength is considered. Depending on the parameter of the logistic family and the strength of coupling, we show the existence of a forward invariant curve which determines, in some sense, the boundary of the set whose points have unbounded orbit.

Revista de la Unión Matemática Argentina

In this article we give a geometric classification of the set of quadratic maps of the plane. The... more In this article we give a geometric classification of the set of quadratic maps of the plane. The fundamental step is the proof that the restriction of the map to the critica! set is injective, from which it follows that there are finitely many classes of geometrically equivalent maps. In the last sections we apply this geometric knowledge to obtain some simple dynamical properties of a particular family of quadratic maps.

Publicaciones En Ciencias Y Tecnologia, 2012

Este artículo, de carácter narrativo y desde una perspectiva personal, tiene por finalidad relata... more Este artículo, de carácter narrativo y desde una perspectiva personal, tiene por finalidad relatar la secuencia de eventos, en términos de programas de formación de matemáticos en la región centro occidental de Venezuela, que han conducido hasta la puesta en marcha del doctorado en matemática en la Universidad Centroccidental Lisandro Alvarado. Se exponen también algunas reflexiones sobre la actividad matemática en esta universidad.

Nonlinearity, 2001

ABSTRACT

Fundamenta Mathematicae, 2007

Sufficient conditions for a map having nonwandering critical points to be Ω-stable are introduced... more Sufficient conditions for a map having nonwandering critical points to be Ω-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of Ω-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom A maps that have no cycles but are not Ω-stable.

Ergodic Theory and Dynamical Systems, 1995

In this paper we extend to a very general context Newhouse's phenomenon concerning the persis... more In this paper we extend to a very general context Newhouse's phenomenon concerning the persistence of homoclinic tangencies and the coexistence of infinitely many sinks. This is done using the corresponding results in codimension one recently provedby J. Palis and M. Viana, and in a reduction of codimension in the unfolding of homoclinic tangencies developed in the present paper.

Discrete and Continuous Dynamical Systems - Series B, 2003

In this paper we provide sufficient conditions in order to show that the set image of a continuou... more In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is injective, then its inverse is also continuous and shift-commuting.

Gaceta Técnica, 2010

In this paper the Smith normal form of certain matrices is used to provide another char acterizat... more In this paper the Smith normal form of certain matrices is used to provide another char acterization for the surjectivity of one-dimensional linear cellular automata with multiple local rules over the ring ZN of integers modulo N = 2.. We reached this goal through an adaptation of a well known result of G. A. Hedlund which characterize the surjectivity of general one-dimensional cellular automata. // RESUMEN: En este artículo es empleada la forma normal de Smith de ciertas matrices para ofrecer otra caracterización de la sobreyectividad de autómatas celulares lineales unidimensionales con múltiples reglas local sobre el anillo ZN de los enteros módulo N = 2. El objetivo es logrado mediante la adaptación de un conocido resultado de G. A. Hedlund que caracteriza la sobreyectividad de autómatas celulares unidimensionales en general.

Acta Mathematica Sinica, English Series, 2018

In this paper, we deal with one-parameter families of real cellular automata in ℝ2. We prove that... more In this paper, we deal with one-parameter families of real cellular automata in ℝ2. We prove that for a wide class of block functions from ℝ2 to ℝ, the corresponding real cellular automaton is expanding when the value of the parameter is large enough.

Topology and its Applications

Abstract Expansive branched covering maps of compact connected surfaces are considered. It is sho... more Abstract Expansive branched covering maps of compact connected surfaces are considered. It is shown that such a map cannot have critical points, so the map is a covering; only the torus and the Klein bottle admit noninvertible expansive covering maps.

This essay was published in Principia: Journal of Culture of the University Lisandro Alvarado. 15... more This essay was published in Principia: Journal of Culture of the University Lisandro Alvarado. 15 (2007), 25-37. The same was stimulated by the fearful anxiety of presenting some lines for the work of mathematicians. They were written based on a series of quotations and ideas readings taken after several trials and books, which in some way or another expose both virtue and the need to maintain in execution of work on which Math and others developed the so-called pure science. Some adjustments have been made ??to the original article, and some lines have been rewritten. My gratitude to the referee, who with his observations enriched this essay.

This paper has a double goal, the first one is to make a slight survey of some theoretical result... more This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary in the context of coupled logistic map. The second goal, in the same context, is to show a collection of figures obtained from computational simulation that reveal the complexity of that dynamical systems.