<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332021000200237</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v28i2.44748</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Índice de conley y sistemas dinámicos continuos]]></article-title>
<article-title xml:lang="en"><![CDATA[Conley Index and continuous dynamical systems]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Zapata Gómez]]></surname>
<given-names><![CDATA[Yesenia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Dela-Rosa]]></surname>
<given-names><![CDATA[Miguel Angel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Remigio-Juárez]]></surname>
<given-names><![CDATA[Jair]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Juárez Autónoma de Tabasco  División Académica de Ciencias Básicas]]></institution>
<addr-line><![CDATA[Cunduacán Tabasco]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Consejo Nacional de Ciencia y Tecnología y Universidad Juárez Autónoma de Tabasco  División Académica de Ciencias Básicas]]></institution>
<addr-line><![CDATA[Cunduacán Tabasco]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Juárez Autónoma de Tabasco  División Académica de Ciencias Básicas]]></institution>
<addr-line><![CDATA[Cunduacán Tabasco]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>28</volume>
<numero>2</numero>
<fpage>237</fpage>
<lpage>259</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332021000200237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332021000200237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332021000200237&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo principal de este trabajo es aplicar métodos topológicos para obtener resultados sobre flujos continuos determinados por ecuaciones diferenciales. Específicamente, aplicamos la teoría del índice de Conley para demostrar que, bajo ciertas condiciones, existe un conjunto invariante que contiene una solución no trivial. La construcción de este conjunto invariante es puramente topológica y depende del flujo de la ecuación diferencial, pero la existencia de la solucion no trivial se obtiene como una aplicación de técnicas de homología. En este artículo expositivo desarrollamos y precisamos estas ideas, y para conseguir un mejor entendimiento incluimos algunos ejemplos y cálculos en algunas ecuaciones diferenciales ordinarias. Este trabajo está basado principalmente en [6].]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The goal of this work is to apply topological methods to obtain results about continuous flows determined by differential equations. Specifically, we apply the Conley Index Theory to prove that, under certain assumptions, there is an invariant set which contains a non-trivial solution. The construction of this invariant set is purely topological and depends on the flow of the differential equation, but the existence of the non-trivial solution is obtained as an application of homological techniques. In this survey paper we develop and precise these ideas, and in order to get a better understanding we include some examples and computations in some ordinary differential equations. This work is mostly based on [6].]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[índice de Conley]]></kwd>
<kwd lng="es"><![CDATA[homología]]></kwd>
<kwd lng="es"><![CDATA[dinámica continua]]></kwd>
<kwd lng="es"><![CDATA[equivalencia homotópica]]></kwd>
<kwd lng="es"><![CDATA[principio de Wazewski.]]></kwd>
<kwd lng="en"><![CDATA[Conley index]]></kwd>
<kwd lng="en"><![CDATA[homology]]></kwd>
<kwd lng="en"><![CDATA[continuous dynamics]]></kwd>
<kwd lng="en"><![CDATA[homotopic equivalence]]></kwd>
<kwd lng="en"><![CDATA[Wazewski principle.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A,V]]></surname>
<given-names><![CDATA[Bolsinov]]></given-names>
</name>
<name>
<surname><![CDATA[A,V]]></surname>
<given-names><![CDATA[Borisov]]></given-names>
</name>
<name>
<surname><![CDATA[I,S]]></surname>
<given-names><![CDATA[Mamaev.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bifurcation analysis and the Conley index in mechanics]]></article-title>
<source><![CDATA[Regular and Chaotic Dynamics]]></source>
<year>2012</year>
<volume>17</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>451-78</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Hatcher.]]></given-names>
</name>
</person-group>
<source><![CDATA[Algebraic Topology]]></source>
<year>2002</year>
<publisher-loc><![CDATA[Ithaca NY ]]></publisher-loc>
<publisher-name><![CDATA[Cornell University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[M,W]]></surname>
<given-names><![CDATA[Hirsch]]></given-names>
</name>
<name>
<surname><![CDATA[R,L]]></surname>
<given-names><![CDATA[Devaney]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Smale.]]></given-names>
</name>
</person-group>
<collab>Pure and Applied Mathematics Series</collab>
<source><![CDATA[Differential Equations, Dynamical Systems, and Linear Algebra]]></source>
<year>2003</year>
<edition>2nd</edition>
<publisher-loc><![CDATA[San Diego ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[T]]></surname>
<given-names><![CDATA[Kaczynski]]></given-names>
</name>
<name>
<surname><![CDATA[K]]></surname>
<given-names><![CDATA[Mischaikow]]></given-names>
</name>
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Mrozek.]]></given-names>
</name>
</person-group>
<collab>Applied Mathematical Sciences</collab>
<source><![CDATA[Computational Homology]]></source>
<year>2004</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Massey.]]></surname>
<given-names><![CDATA[W,S]]></given-names>
</name>
</person-group>
<collab>Graduate Texts in Mathematics</collab>
<source><![CDATA[A Basic Course in Algebraic Topology]]></source>
<year>1991</year>
<publisher-loc><![CDATA[New York NY ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[K]]></surname>
<given-names><![CDATA[Mischaikow]]></given-names>
</name>
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Mrozek.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conley index]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Fiedler]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of Dynamical Systems]]></source>
<year>2002</year>
<volume>2</volume>
<page-range>393-460</page-range><publisher-name><![CDATA[Elsevier Science]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Perko.]]></given-names>
</name>
</person-group>
<collab>Texts in Applied Mathematics</collab>
<source><![CDATA[Differential Equations and Dynamical Systems]]></source>
<year>2008</year>
<publisher-loc><![CDATA[New York NY ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
