{"id":1905,"date":"2014-02-10T13:24:45","date_gmt":"2014-02-10T16:24:45","guid":{"rendered":"http:\/\/www.complejidadsocial.udd.cl\/?p=1905"},"modified":"2014-02-10T13:24:45","modified_gmt":"2014-02-10T16:24:45","slug":"sums-of-variables-at-the-onset-of-chaos","status":"publish","type":"post","link":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/","title":{"rendered":"Sums of variables at the onset of chaos"},"content":{"rendered":"<p>Miguel Angel Fuentes and Alberto Robledo. <span class=\"st\">The European Physical Journal B. <\/span>DOI:10.1140\/epjb\/e2014-40882-1.<\/p>\n<p><strong>ABSTRACT<\/strong><\/p>\n<p>We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.<\/p>\n<p><span class=\"st\"><span lang=\"JA\" style=\"color: #0000ff; font-family: CMR9; font-size: xx-small;\"><span lang=\"JA\" style=\"color: #0000ff; font-family: CMR9; font-size: xx-small;\"><span lang=\"JA\" style=\"color: #0000ff; font-family: CMR9; font-size: xx-small;\"><span lang=\"JA\" style=\"color: #131413; font-family: CMR9; font-size: xx-small;\"><span lang=\"JA\" style=\"color: #131413; font-family: CMR9; font-size: xx-small;\"><span lang=\"JA\" style=\"color: #131413; font-family: CMR9; font-size: xx-small;\"><a href=\"https:\/\/gobierno.udd.cl\/cics\/files\/2014\/07\/MF-The-European-Physical-Journal.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-85\" src=\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\" alt=\"PDF\" width=\"40\" height=\"40\" \/><\/a><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"font: 13px\/19.5px Arial, Verdana, sans-serif; text-align: left; color: #333333; text-transform: none; text-indent: 0px; letter-spacing: normal; word-spacing: 0px; float: none; display: inline !important; white-space: normal; background-color: #ffffff; -webkit-text-stroke-width: 0px;\">Do not disseminate\/print without permission of copyright holder.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Miguel Angel Fuentes and Alberto Robledo. The European Physical Journal B. DOI:10.1140\/epjb\/e2014-40882-1. ABSTRACT We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed [&hellip;]<\/p>\n","protected":false},"author":9192218,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,5],"tags":[],"class_list":["post-1905","post","type-post","status-publish","format-standard","hentry","category-papers","category-publications"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Sums of variables at the onset of chaos - Centro de Investigaci\u00f3n en Complejidad Social<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sums of variables at the onset of chaos - Centro de Investigaci\u00f3n en Complejidad Social\" \/>\n<meta property=\"og:description\" content=\"Miguel Angel Fuentes and Alberto Robledo. The European Physical Journal B. DOI:10.1140\/epjb\/e2014-40882-1. ABSTRACT We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\" \/>\n<meta property=\"og:site_name\" content=\"Centro de Investigaci\u00f3n en Complejidad Social\" \/>\n<meta property=\"article:published_time\" content=\"2014-02-10T16:24:45+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\" \/>\n<meta name=\"author\" content=\"mariapia.kralemann\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mariapia.kralemann\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\"},\"author\":{\"name\":\"mariapia.kralemann\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/129ad217f6071913cdd7514153362439\"},\"headline\":\"Sums of variables at the onset of chaos\",\"datePublished\":\"2014-02-10T16:24:45+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\"},\"wordCount\":166,\"commentCount\":0,\"image\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"articleSection\":[\"PAPERS\",\"PUBLICATIONS\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\",\"url\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\",\"name\":\"Sums of variables at the onset of chaos - Centro de Investigaci\u00f3n en Complejidad Social\",\"isPartOf\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"datePublished\":\"2014-02-10T16:24:45+00:00\",\"author\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/129ad217f6071913cdd7514153362439\"},\"breadcrumb\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage\",\"url\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"contentUrl\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"width\":40,\"height\":40},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/gobierno.udd.cl\/cics\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Sums of variables at the onset of chaos\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#website\",\"url\":\"https:\/\/gobierno.udd.cl\/cics\/\",\"name\":\"Centro de Investigaci\u00f3n en Complejidad Social\",\"description\":\"Facultad de Gobierno - Universidad del Desarrollo\",\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/129ad217f6071913cdd7514153362439\",\"name\":\"mariapia.kralemann\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/bf4b4abb210f68fa431d2c576edd63353f267ddb163364553f04cf5df5f6cb32?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/bf4b4abb210f68fa431d2c576edd63353f267ddb163364553f04cf5df5f6cb32?s=96&d=mm&r=g\",\"caption\":\"mariapia.kralemann\"},\"url\":\"https:\/\/gobierno.udd.cl\/cics\/author\/mariapia-kralemann\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Sums of variables at the onset of chaos - Centro de Investigaci\u00f3n en Complejidad Social","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/","og_locale":"en_US","og_type":"article","og_title":"Sums of variables at the onset of chaos - Centro de Investigaci\u00f3n en Complejidad Social","og_description":"Miguel Angel Fuentes and Alberto Robledo. The European Physical Journal B. DOI:10.1140\/epjb\/e2014-40882-1. ABSTRACT We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed [&hellip;]","og_url":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/","og_site_name":"Centro de Investigaci\u00f3n en Complejidad Social","article_published_time":"2014-02-10T16:24:45+00:00","og_image":[{"url":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","type":"","width":"","height":""}],"author":"mariapia.kralemann","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mariapia.kralemann","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#article","isPartOf":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/"},"author":{"name":"mariapia.kralemann","@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/129ad217f6071913cdd7514153362439"},"headline":"Sums of variables at the onset of chaos","datePublished":"2014-02-10T16:24:45+00:00","mainEntityOfPage":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/"},"wordCount":166,"commentCount":0,"image":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage"},"thumbnailUrl":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","articleSection":["PAPERS","PUBLICATIONS"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/","url":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/","name":"Sums of variables at the onset of chaos - Centro de Investigaci\u00f3n en Complejidad Social","isPartOf":{"@id":"https:\/\/gobierno.udd.cl\/cics\/#website"},"primaryImageOfPage":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage"},"image":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage"},"thumbnailUrl":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","datePublished":"2014-02-10T16:24:45+00:00","author":{"@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/129ad217f6071913cdd7514153362439"},"breadcrumb":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#primaryimage","url":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","contentUrl":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","width":40,"height":40},{"@type":"BreadcrumbList","@id":"https:\/\/gobierno.udd.cl\/cics\/2014\/02\/10\/sums-of-variables-at-the-onset-of-chaos\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/gobierno.udd.cl\/cics\/"},{"@type":"ListItem","position":2,"name":"Sums of variables at the onset of chaos"}]},{"@type":"WebSite","@id":"https:\/\/gobierno.udd.cl\/cics\/#website","url":"https:\/\/gobierno.udd.cl\/cics\/","name":"Centro de Investigaci\u00f3n en Complejidad Social","description":"Facultad de Gobierno - Universidad del Desarrollo","inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/129ad217f6071913cdd7514153362439","name":"mariapia.kralemann","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/bf4b4abb210f68fa431d2c576edd63353f267ddb163364553f04cf5df5f6cb32?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/bf4b4abb210f68fa431d2c576edd63353f267ddb163364553f04cf5df5f6cb32?s=96&d=mm&r=g","caption":"mariapia.kralemann"},"url":"https:\/\/gobierno.udd.cl\/cics\/author\/mariapia-kralemann\/"}]}},"featured_image_url":null,"_links":{"self":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/posts\/1905","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/users\/9192218"}],"replies":[{"embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/comments?post=1905"}],"version-history":[{"count":0,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/posts\/1905\/revisions"}],"wp:attachment":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/media?parent=1905"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/categories?post=1905"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/tags?post=1905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}