{"id":597,"date":"2025-09-03T15:27:15","date_gmt":"2025-09-03T14:27:15","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=597"},"modified":"2025-09-03T15:27:15","modified_gmt":"2025-09-03T14:27:15","slug":"especies-competidores-i-homeomorfismes-del-disc","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/especies-competidores-i-homeomorfismes-del-disc\/","title":{"rendered":"Esp\u00e8cies competidores i homeomorfismes del disc"},"content":{"rendered":"\n<p>L&#8217;objectiu d&#8217;aquest treball \u00e9s aprofundir en els detalls del curs <em>Competing species and homeomorphisms of the disc\u00a0<\/em>del Professor Rafael Ortega (M\u00e1laga, 2007).<\/p>\n<p>En aquest curs es mostra com la Topologia \u00e9s \u00fatil per entendre el comportament din\u00e0mic de sistemes d&#8217;equacions diferencials (en aquest cas, sistemes que modelen la interacci\u00f3 entre diferents esp\u00e8cies) quan nom\u00e9s tenim informaci\u00f3 qualitativa del sistema (\u00e9s a dir, no tenim l&#8217;expressi\u00f3 de les equacions per\u00f2 s\u00ed el comportament qualitatiu de les funcions que les formen).<\/p>\n<p>El curs est\u00e0 enfocat a una pregunta concreta: el principi d&#8217;exclusi\u00f3 competitiva. Si diferents esp\u00e8cies competeixen per un mateix recurs, alguna d&#8217;elles s&#8217;ha d&#8217;extingir? Aquesta pregunta est\u00e0 relacionada amb el seg\u00fcent problema: Sigui \\(h: B \\rightarrow B\\) un homeomorphisme de la bola unitat \\(B=\\{x\\in\\mathbb{R}^d : \\|x\\|\\leq 1\\}\\) que preserva la orientaci\u00f3. Suposa que tots els seus punts fixos estan a la frontera, \\(Fix(h)\\subset\\partial B\\). Podem dir que totes les \u00f2rbites \\(h^n(p)\\) han d&#8217;anar a parar a \\(\\partial B\\)?<\/p>\n<p>En el treball s&#8217;entrar\u00e0 en els detalls d&#8217;aquest curs, omplint els detalls que falten, i s&#8217;introduir\u00e0 la <em>Teoria de Brouwer de traslaci\u00f3 d&#8217;arcs.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>L&#8217;objectiu d&#8217;aquest treball \u00e9s aprofundir en els detalls del curs Competing species and homeomorphisms of the disc\u00a0del Professor Rafael Ortega (M\u00e1laga, 2007). En aquest curs es mostra com la Topologia \u00e9s \u00fatil per entendre el comportament din\u00e0mic de sistemes d&#8217;equacions diferencials (en aquest cas, sistemes que modelen la interacci\u00f3 entre diferents esp\u00e8cies) quan nom\u00e9s tenim [&hellip;]<\/p>\n","protected":false},"author":85,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31,30],"tags":[51],"class_list":["post-597","post","type-post","status-publish","format-standard","hentry","category-geometria-i-topologia","category-matematica-aplicada","tag-david-rojas"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/597","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=597"}],"version-history":[{"count":2,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/597\/revisions"}],"predecessor-version":[{"id":599,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/597\/revisions\/599"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=597"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}