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1. Verfasser:	Michael Rojas Romero
Format:	Artículo científico
Sprache:	es
Veröffentlicht:	Universidad Autónoma de Ciudad Juárez 2015
Schlagworte:	Multidisciplinarias (Ciencias Sociales) orbita iteración punto fijo Mathematica Palabras clave
Online-Zugang:	https://www.redalyc.org/articulo.oa?id=85932588009
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Una aproximación experimental a los sistemas dinámicos discretos con Mathematica Michael Rojas Romero Multidisciplinarias (Ciencias Sociales) orbita iteración punto fijo Mathematica Palabras clave Experimentar con sistemas dinámicos a tiempo discreto, puede representar un recurso didáctico importante en la investigación de las propiedades de los sistemas dinámicos y de sus posibles aplicaciones a disciplinas como la economía. Como una ilustración de esta posibilidad didáctica, en este documento se presenta una breve introducción a la actividad de los sistemas dinámicos a tiempo discreto mediante ejemplos asistidos por el lenguaje simbólico Mathematica. Dichos sistemas son esencialmente mapas itera - dos. En una primera parte, construimos órbitas de puntos bajo iteración de funciones reales y complejas. Si x es un número real o un número complejo, entonces la órbita de x bajo f es la sucesión {x, f(x), f(f(x)),...} . Estas sucesiones pueden ser convergentes o sucesiones que tienden a infinito. En particular, para probar este comportamiento en sucesiones complejas, será necesario el concepto de derivada de una función compleja. En una segunda parte, utilizamos los conceptos revisados en la primera para construir conjuntos Julia, éstos se adquieren de asignar colores a los puntos en una malla rectan - gular de acuerdo al comportamiento de sus órbitas bajo la función compleja estudiada, los colores se asignan de acuerdo a la clasificación de los puntos. El dibujo obtenido, el conjunto Julia, es un fractal. No obstante, la imagen que se logra será siempre una aproximación. 2015 artículo científico 0188-9834 https://www.redalyc.org/articulo.oa?id=85932588009 es http://www.redalyc.org/revista.oa?id=859 NÓESIS. REVISTA DE CIENCIAS SOCIALES Y HUMANIDADES application/pdf Universidad Autónoma de Ciudad Juárez NÓESIS. REVISTA DE CIENCIAS SOCIALES Y HUMANIDADES (México) Num.47 Vol.24

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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