<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2007-8064</journal-id>
<journal-title><![CDATA[Entreciencias: diálogos en la sociedad del conocimiento]]></journal-title>
<abbrev-journal-title><![CDATA[Entreciencias: diálogos soc. conoc.]]></abbrev-journal-title>
<issn>2007-8064</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Escuela Nacional de Estudios Superiores]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-80642019000100011</article-id>
<article-id pub-id-type="doi">10.22201/enesl.20078064e.2018.19.65822</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estudio de una familia de funciones de periodo tres y su dinámica caótica]]></article-title>
<article-title xml:lang="en"><![CDATA[Study of a family of period three functions and its chaotic dynamics]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Macías Ponce]]></surname>
<given-names><![CDATA[Julio César]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez Álvarez]]></surname>
<given-names><![CDATA[Luis Fernando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Aguascalientes  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2019</year>
</pub-date>
<volume>7</volume>
<numero>19</numero>
<fpage>11</fpage>
<lpage>25</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-80642019000100011&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-80642019000100011&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-80642019000100011&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Objetivo: construir sistemas dinámicos caóticos unidimensionales mediante el estudio de una familia de funciones con dominio y contradominio en el intervalo [0,1] la cual se define en términos de cuatro parámetros.  Método: con base a los parámetros que definen a cada función que proponemos, se identificaron aquellas que tienen periodo tres, las cuales inducen un sistema caótico en el contexto de Li-Yorke. Los teoremas del punto fijo y de Sharkovskii fueron la herramienta fundamental de nuestro trabajo.  Resultados: se obtuvo un conjunto de sistemas dinámicos caóticos, se describió un procedimiento sencillo para obtener sistemas dinámicos caóticos (adicionales a los obtenidos) y se sugiere como primera aplicación la obtención de números pseudoaleatorios.  Limitaciones: los sistemas dinámicos construidos son caóticos en el sentido de Li-Yorke, -no necesariamente en el sentido de Devaney-.  Principales hallazgos: las funciones estudiadas tienen una gráfica en forma de Zeta, y para cada una de ellas se identifica a su respectiva dual (las gráficas que se obtienen presentan una relación de simetría), de esta manera se muestran las condiciones que deben verificar los parámetros -primal y dual- para obtener (y no obtener) período tres.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Purpose: To build one-dimensional chaotic dynamical systems through the study of functions with domain and codomain in the interval [0, 1] which is defined in terms of four parameters.  Methodology: Based on the parameters that define each function that is proposed, those which have period three were identified and which induce a chaotic system in the context of Li-Yorke. The fixed point and Sharkovskii theorems were the fundamental tools in this work.  Results: We obtained a set of chaotic dynamic systems. In turn, we described a simple process in order to obtain chaotic dynamic systems (additional to those obtained) and we suggest, as a first application, the obtainment of pseudo-random numbers.  Limitations: The dynamic systems that were built are chaotic in the Li-Yorke sense -not necessarily in the Devaney sense-.  Findings: The functions that were studied have a Zeta form graphic, and for each of those we identified its respective dual (the obtained graphics present a symmetric relation) and that is how we show the conditions that must verify the parameters -primal and dual- in order to obtain (or not) period three.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[caos]]></kwd>
<kwd lng="es"><![CDATA[Sharkovskii]]></kwd>
<kwd lng="es"><![CDATA[sistemas dinámicos]]></kwd>
<kwd lng="es"><![CDATA[órbita]]></kwd>
<kwd lng="en"><![CDATA[Chaos]]></kwd>
<kwd lng="en"><![CDATA[Sharkovskii]]></kwd>
<kwd lng="en"><![CDATA[dynamic systems]]></kwd>
<kwd lng="en"><![CDATA[orbit]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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