<?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>1645-9911</journal-id>
<journal-title><![CDATA[Tékhne - Revista de Estudos Politécnicos]]></journal-title>
<abbrev-journal-title><![CDATA[Tékhne]]></abbrev-journal-title>
<issn>1645-9911</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico do  Cávado e do Ave]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1645-99112007000200009</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Dinâmica simbólica e ferradura de Smale]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ferreira]]></surname>
<given-names><![CDATA[Fernanda Amélia]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Instituto Politécnico do Porto ESEIG - Escola Superior de Estudos Industriais e de Gestão ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2007</year>
</pub-date>
<numero>8</numero>
<fpage>183</fpage>
<lpage>199</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_arttext&amp;pid=S1645-99112007000200009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_abstract&amp;pid=S1645-99112007000200009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_pdf&amp;pid=S1645-99112007000200009&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Descrevemos a "ferradura de Smale", um sistema dinâmico bem conhecido que apresenta um conjunto de propriedades muito importantes em Sistemas Dinâmicos. O estudo da dinâmica da "ferradura de Smale" permitenos entender a importância do conceito de dinâmica simbólica.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[We describe the Smale horseshoe, a well-known dynamical system that presents a set of properties which are very important in Dynamical Systems. The study of the dynamics of the Smale horseshoe allows us to understand the importance of the notion of symbolic dynamics.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Sistemas Dinâmicos]]></kwd>
<kwd lng="pt"><![CDATA[Ferradura de Smale]]></kwd>
<kwd lng="pt"><![CDATA[Dinâmica simbólica]]></kwd>
<kwd lng="en"><![CDATA[Dynamical Systems]]></kwd>
<kwd lng="en"><![CDATA[Smale horseshoe]]></kwd>
<kwd lng="en"><![CDATA[Symbolic dynamics]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="center"><b>Din&acirc;mica simb&oacute;lica e ferradura de Smale    </b></p>     <p align="center">Fernanda Am&eacute;lia Ferreira<a href="#1">*</a> <a name="top1"></a></p>     <p align="center"><a href="mailto:fernandaamelia@eseig.ipp.pt%20">fernandaamelia@eseig.ipp.pt    </a></p>     <p align="center">(recebido em 22 de Mar&ccedil;o de 2007; aceite em 22 de Outubro    de 2007) </p>     <p align="center">&nbsp;</p>     <p align="justify"><b>Resumo</b>: Descrevemos a &#8220;ferradura de    Smale&#8221;, um sistema din&acirc;mico bem conhecido que apresenta um conjunto    de propriedades muito importantes em Sistemas Din&acirc;micos. O estudo da din&acirc;mica    da &#8220;ferradura de Smale&#8221; permitenos entender a import&acirc;ncia    do conceito de din&acirc;mica simb&oacute;lica.</p>     <p align="justify"><b>Palavras-chave</b>: Sistemas Din&acirc;micos,    Ferradura de Smale, Din&acirc;mica simb&oacute;lica</p>     <p align="justify">&nbsp;</p>     <p align="justify"><b>Abstract</b>: We describe the Smale horseshoe,    a well-known dynamical system that presents a set of properties which are very    important in Dynamical Systems. The study of the dynamics of the Smale horseshoe    allows us to understand the importance of the notion of symbolic dynamics.</p>     <p align="justify"> <b>Keywords</b>: Dynamical Systems, Smale horseshoe, Symbolic    dynamics</p>     ]]></body>
<body><![CDATA[<p align="justify">&nbsp;</p>     <p align="justify">Texto completo dispon&iacute;vel apenas em PDF.</p>     <p>Full text only available in PDF format. </p>     <p>&nbsp;</p>     <p><b>Refer&ecirc;ncias Bibliogr&aacute;ficas</b></p>     <!-- ref --><p align="justify"> Cartwright, M. L. and Littlewood, J. E. (1945) On Non-Linear    Differential Equations of the Second Order, <i>J. London Math. Soc.</i> 20,    180-189.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000018&pid=S1645-9911200700020000900001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p align="justify"> Ferreira, F. A. (2002) <i>Din&acirc;mica n&atilde;o linear:    Atractores</i>. Disserta&ccedil;&atilde;o de Mestrado, Universidade Portucalense:    Porto, Portugal.</p>     <p align="justify"> Ferreira, F. A. and Ferreira, F. (2003) Din&acirc;mica Simb&oacute;lica:    um aux&iacute;lio precioso, Lus&iacute;ada, <i>Revista de Ci&ecirc;ncia e Cultura:    S&eacute;rie de Matem&aacute;tica 1</i>, 35-58.</p>     <p align="justify"> Gleick, J. (1994) <i>Caos: A Constru&ccedil;&atilde;o de    Uma Nova Ci&ecirc;ncia</i>. Gradiva: Lisboa.</p>     <p align="justify"> Levinson, N. (1949) Determination of the Potential from the    Asymptotic Phase, <i>Physical Review </i>75, 1445-1445.</p>     ]]></body>
<body><![CDATA[<p align="justify"> van der Pol, B. and van der Mark, J. (1927), Frequency demultiplication,    <i>Nature</i> 120, 363- 364.</p>     <p align="justify"> Rayleigh, J. W. S. (1896) Theoretical considerations respecting    the separation of gases by diffusion and similar processes, <i>Philosophical    Magazine and Journal of Science</i> 42, 493&#8211; 498.</p>     <p align="justify"> Robinson, C. (1999) <i>Dynamical Systems: Stability, Symbolic    Dynamics, and Chaos</i>. CRC Press LLC: New York.</p>     <p align="justify"> Smale, S. (1963) <i>Stable manifolds for differential equations    and diffeomorphisms</i>. Ann. Scuola Normale Pisa 18, 97-116.</p>     <p align="justify"> Smale, S. (1980) <i>The Mathematics of Time: Essays on Dynamical    Systems, Economic Processes, and Related Topics</i>. Springer-Verlag: New York,    Heidelberg, Berlin.</p>     <p align="justify"> Stewart, I. (2000) <i>Deus Joga aos Dados? </i>Ci&ecirc;ncia    Aberta. Gradiva: Lisboa.</p>     <p align="justify"> [1] <a href="http://www.led.ufba.br/calculo3/turbulencia/dinamico.htm" target="_blank">http://www.led.ufba.br/calculo3/turbulencia/dinamico.htm</a>    (consultado em 04-06-2002).</p>     <p align="justify"> [2] <a href="http://www.uol.com.br/cienciahoje/ch/ch156.htm" target="_blank">http://www.uol.com.br/cienciahoje/ch/ch156.htm</a>    (consultado em 04-06-2002).</p>     <p align="justify">&nbsp;</p>     <p align="justify"><b>Outra Bibliografia Consultada</b></p>     ]]></body>
<body><![CDATA[<p align="justify">Arrowsmith, D. K. and Place, C. M. (1991) <i>An Introduction    to Dynamical Systems</i>. Cambridge University Press: Cambridge.</p>     <p align="justify"> Broer H. W. and Dumortier F. (1991) <i>Genericity and Structural    Stability</i>. North-Holland: Amsterdam.</p>     <p align="justify"> Devaney, R. L. (1989) <i>An Introduction to Chaotic Dynamical    Systems</i>. Addison-Wesley Publishing Company: New York.</p>     <p align="justify"> Guckenheimer, J. and Holmes, P. (1997) <i>Nonlinear Oscillations,    Dynamical Systems, and Bifurcations of Vector Fields</i>. Springer-Verlag:    New York.</p>     <p align="justify"> Hirsch, M. W. and Smale, S. (1974) <i>Differential Equations,    Dynamical Systems, and Linear Algebra</i>. Academic Press: New York.</p>     <p align="justify"> Irwin, M. C. (1980) <i>Smooth Dynamical Systems</i>. Academic    Press: New York.</p>     <p align="justify"> Palis, J. and de Melo, W. (1978) <i>Introdu&ccedil;&atilde;o    aos Sistemas Din&acirc;micos</i>. Editora Edgard Blucher, Ltda., S&atilde;o    Paulo.</p>     <p align="justify"> Shub, M. (1987) <i>Global Stability of Dynamical Systems</i>.    Springer-Verlag: New York, Heidelberg, Berlin.</p>     <p align="justify">&nbsp;</p>     <p align="justify"><a href="#top1">*</a><a name="1"></a>ESEIG - Escola Superior    de Estudos Industriais e de Gest&atilde;o, Instituto Polit&eacute;cnico do Porto</p>     ]]></body>
<body><![CDATA[<p align="justify">&nbsp;</p>     <p align="center">&nbsp;</p>     <p align="justify">&nbsp;</p>      ]]></body><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cartwright]]></surname>
<given-names><![CDATA[M. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Littlewood]]></surname>
<given-names><![CDATA[J. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[On Non-Linear Differential Equations of the Second Order]]></article-title>
<source><![CDATA[J. London Math. Soc.]]></source>
<year>1945</year>
<numero>20</numero>
<issue>20</issue>
<page-range>180-189</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
