{"id":14528,"date":"2024-10-08T11:32:00","date_gmt":"2024-10-08T16:32:00","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=14528"},"modified":"2024-10-08T11:32:00","modified_gmt":"2024-10-08T16:32:00","slug":"graduate-student-colloquium-kelsey-brouwer","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-kelsey-brouwer\/","title":{"rendered":"Graduate Student Colloquium: Kelsey Brouwer"},"content":{"rendered":"

<\/h1>\n

Combinatorial Models for Some Generalized McMullen Maps in the Case of Two Bounded Critical Orbits<\/h1>\n

Kelsey Brouwer
\nPhD Student<\/em>
\nUniversity of Wisconsin – Milwaukee<\/p>\n

The family of generalized McMullen maps R(z)= z^n + b + a\/z^n has two independent critical orbits. We consider the case in which one critical value lies in the immediate basin of an attracting cycle and the other critical value eventually lands in that immediate basin. Computer-generated images of the dynamical plane suggest the presence of both baby quadratic Julia sets and some sets which appear to be modifications of those. We present combinatorial models of the dynamics which help to explain this phenomena.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Combinatorial Models for Some Generalized McMullen Maps in the Case of Two Bounded Critical Orbits Kelsey Brouwer PhD Student University of Wisconsin – Milwaukee The family of generalized McMullen maps R(z)= z^n + b + a\/z^n has two independent critical …<\/p>\n","protected":false},"author":4217,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[70],"class_list":["post-14528","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-graduate-student-colloquia","cat_graduate-student-colloquia"],"yoast_head":"\nMathematical Sciences<\/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:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-kelsey-brouwer\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Graduate Student Colloquium: Kelsey Brouwer\" \/>\n<meta property=\"og:description\" content=\"Combinatorial Models for Some Generalized McMullen Maps in the Case of Two Bounded Critical Orbits Kelsey Brouwer PhD Student University of Wisconsin – Milwaukee The family of generalized McMullen maps R(z)= z^n + b + a\/z^n has two independent critical …\" \/>\n<meta property=\"og:url\" content=\"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-kelsey-brouwer\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathematical Sciences\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/graduate-student-colloquium-kelsey-brouwer\\\/\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/graduate-student-colloquium-kelsey-brouwer\\\/\",\"name\":\"Graduate Student Colloquium: Kelsey Brouwer - 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