{"id":592,"date":"2025-09-03T14:36:12","date_gmt":"2025-09-03T13:36:12","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=592"},"modified":"2025-09-03T14:36:12","modified_gmt":"2025-09-03T13:36:12","slug":"estudi-dinamic-de-laplicacio-logistica","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/estudi-dinamic-de-laplicacio-logistica\/","title":{"rendered":"Estudi din\u00e0mic de l&#8217;aplicaci\u00f3 log\u00edstica"},"content":{"rendered":"\n<p>L&#8217;objectiu d&#8217;aquest treball \u00e9s realitzar un estudi de la din\u00e0mica produ\u00efda pel sistema din\u00e0mic discret $$x_{n+1} = F_{\\mu}(x_n),$$ on \\(F_{\\mu}(x) = \\mu x (1-x)\\), en funci\u00f3 del par\u00e0metre \\(\\mu&gt;0\\).<\/p>\n<p>Per valors del par\u00e0metre \\(\\mu\\in(0,3)\\) la din\u00e0mica \u00e9s essencialment trivial i pot ser descrita sense grans tecnicismes. A mesura que el par\u00e0metre augmenta dins l&#8217;interval \\((3,4)\\) la din\u00e0mica deixa de ser senzilla, apareixent \u00f2rbites peri\u00f2diques de diferents per\u00edodes (en l&#8217;ordre de <em>Sarkovskii<\/em>) en el proc\u00e9s conegut com a\u00a0<em>period-doubling cascade.<\/em> Finalment, per par\u00e0metres \\(\\mu&gt;4\\) la din\u00e0mica arriba a ser\u00a0<em>ca\u00f2tica<\/em>.<\/p>\n<p>En aquest treball s&#8217;estudiar\u00e0 la propietat de din\u00e0mica ca\u00f2tica i es provar\u00e0 que l&#8217;aplicaci\u00f3 log\u00edstica \u00e9s ca\u00f2tica per \\(\\mu&gt;4\\). Tamb\u00e9 veurem que dins l&#8217;interval \\((3,4)\\) la complexitat din\u00e0mica augmenta de manera mon\u00f2tona amb el par\u00e0metre, fent servir la <em>din\u00e0mica simb\u00f2lica<\/em> com a eina i la <em>Teoria Kneading<\/em> de Milnor i Thurston.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>L&#8217;objectiu d&#8217;aquest treball \u00e9s realitzar un estudi de la din\u00e0mica produ\u00efda pel sistema din\u00e0mic discret $$x_{n+1} = F_{\\mu}(x_n),$$ on \\(F_{\\mu}(x) = \\mu x (1-x)\\), en funci\u00f3 del par\u00e0metre \\(\\mu&gt;0\\). Per valors del par\u00e0metre \\(\\mu\\in(0,3)\\) la din\u00e0mica \u00e9s essencialment trivial i pot ser descrita sense grans tecnicismes. A mesura que el par\u00e0metre augmenta dins l&#8217;interval \\((3,4)\\) [&hellip;]<\/p>\n","protected":false},"author":85,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30],"tags":[51],"class_list":["post-592","post","type-post","status-publish","format-standard","hentry","category-matematica-aplicada","tag-david-rojas"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/592","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/85"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=592"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/592\/revisions"}],"predecessor-version":[{"id":595,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/592\/revisions\/595"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}