{ "153015-21914925": { "datetime_modified":"20261105T090223", "datetime_start":"20261109T160000", "datetime_end":"20261109T170000", "has_end_time":1, "date_start":"2026-11-09", "date_end":"2026-11-09", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Dynamics seminar: Dynamics of the Secant Method and Other Monomial-Type Maps", "occurrence_title":"", "combined_title":"Dynamics seminar: Dynamics of the Secant Method and Other Monomial-Type Maps: Nick Freeman", "event_subtitle":"Nick Freeman", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "description":"We discuss the secant method, a root-finding algorithm alternative to Newton\u2019s method. Given a rational map f : P^1 -> P^1, the secant method yields a dynamical system Sf on P^1 x P^1 (minus a finite indeterminacy locus). If r in C is a simple root of f, then the point (r, r) is an attracting fixed point of Sf.\n\nAdditionally, when 0 is a simple root of f with f\u2019\u2019(0) nonzero, we have that Sf is an instance of the broader class of \u201cmonomial-type maps.\u201d A \u201cmonomial map\u201d is simply a function whose output coordinates are all monomials in the input coordinates. A \u201cmonomial-type map\u201d is then a coordinate-by-coordinate scaling of a monomial map by some holomorphic scalar functions. In the aforementioned case for 0 and Sf, we find that Sf(x, y) = (a(x, y) * xy, x). \n\nBy extending the 1-dimensional constructions of B\u00f6ttcher coordinates and Green\u2019s functions to these higher-dimensional monomial-type maps, we can show that (1) Sf has well-defined dynamical potential, (2) it takes the vequipotential to the v^\u03c6 equipotential (where \u03c6 is the golden ratio), and (3) Sf is locally modeled by the Fibonacci monomial map (x, y) |-> (xy, x), whose dynamics are well-understood.", "occurrence_notes":null, "guid":"153015-21914925@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/153015", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"3096", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Dynamics"], "website":"", "sponsors":[ { "group_name":"Complex Analysis, Dynamics and Geometry Seminar - Department of Mathematics", "group_id":"4887", "website":"" }, { "group_name":"Department of Mathematics", "group_id":"3791", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21914925 } , "152446-21913750": { "datetime_modified":"20260918T135009", "datetime_start":"20261109T160000", "datetime_end":"20261109T170000", "has_end_time":1, "date_start":"2026-11-09", "date_end":"2026-11-09", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"ECE Diwali Celebration", "occurrence_title":"", "combined_title":"ECE Diwali Celebration", "event_subtitle":"", "event_type":"Social \/ Informal Gathering", "event_type_id":"19", "description":"All ECE students are invited to a Diwali celebration on Monday, November 9th. This event is a great way to learn something new, make new friends with your fellow ECE students, and sample some good food! Music, crafts and a henna artist will be available as well. Bring your MCard!\n\nDiwali is a festival of lights. The festival usually lasts five days, or six in some regions of India.", "occurrence_notes":null, "guid":"152446-21913750@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/152446", "building_id":"1000448", "building_name":"Electrical Engineering and Computer Science Building", "campus_maps_id":"56", "room":"Atrium", "location_name":"Electrical Engineering and Computer Science Building", "has_livestream":0, "cost":"", "tags":["Computer Engineering","Culture","Electrical And Computer Engineering","Electrical Engineering and Computer Science","engineering"], "website":"https:\/\/ece.engin.umich.edu\/event\/ece-diwali-celebration", "sponsors":[ { "group_name":"Electrical and Computer Engineering", "group_id":"3153", "website":"http:\/\/www.ece.engin.umich.edu" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2026\/09\/event_152446_original-1.jpg", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2026\/09\/event_152446_original-1.jpg" }, "occurrence_count":1, "first_occurrence":21913750 } }