{"id":1004,"date":"2019-02-26T16:20:03","date_gmt":"2019-02-27T00:20:03","guid":{"rendered":"http:\/\/blog.ronrecord.com\/?page_id=1004"},"modified":"2019-02-27T14:20:51","modified_gmt":"2019-02-27T22:20:51","slug":"lyapunov-exponents","status":"publish","type":"page","link":"https:\/\/blog.ronrecord.com\/index.php\/lyapunov-exponents\/","title":{"rendered":"Lyapunov Exponents"},"content":{"rendered":"\n<p><strong>These images represent the <\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Lyapunov_exponent\"><strong>Lyapunov exponents<\/strong><\/a><strong> of a forced oscillator modeled by parameterizing the <\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Logistic_map\"><strong>Logistic map<\/strong><\/a><strong>. The Lyapunov exponents of a dynamical system can be used to numerically characterize the qualitative behavior of the system.<\/strong><\/p>\n\n\n\n<p><strong>The images in this gallery were created by Dr. Ronald Joe Record who holds a Ph.D. in Mathematics from the University of California. Dr. Record&#8217;s research focused on applications of Dynamical Systems Theory, an area of Mathematics popularly known as Chaos Theory.<\/strong><\/p>\n\n\n<p>[foogallery id=&#8221;1003&#8243;]<\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"text-align:center\"><b>All photography and digital photo manipulation by Ronald Joe Record, Copyright 2019, all rights reserved.<\/b><\/p><p><table class=\"wp-block-table\" style=\"text-align:center\" width=100% border=0 cellpadding=5 cellspacing=5><tbody><tr><td style=\"text-align:center\"><a href=\"http:\/\/blog.ronrecord.com\/index.php\/mandelbrot-julia-sets\/\"><b>Mandelbrot<\/b><\/a><\/td><td style=\"text-align:center\"><a href=\"http:\/\/blog.ronrecord.com\/index.php\/lyapunov-exponents\/\"><b>Lyapunov<\/b><\/a><\/td><td style=\"text-align:center\"><a href=\"http:\/\/blog.ronrecord.com\/index.php\/iterated-systems\/\"><b>Iterated<\/b><\/a><\/td><td style=\"text-align:center\"><a href=\"http:\/\/blog.ronrecord.com\/index.php\/fractal-art\/\"><b>Fractals<\/b><\/a><\/td><td style=\"text-align:center\"><a href=\"http:\/\/blog.ronrecord.com\/index.php\/psychedelic-photo-art\/\"><b>Photos<\/b><\/a><\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>These images represent the Lyapunov exponents of a forced oscillator modeled by parameterizing the Logistic map. The Lyapunov exponents of a dynamical system can be used to numerically characterize the&hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/1004"}],"collection":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/comments?post=1004"}],"version-history":[{"count":3,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/1004\/revisions"}],"predecessor-version":[{"id":1096,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/1004\/revisions\/1096"}],"wp:attachment":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media?parent=1004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}