BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Marti-Pete (University of Liverpool) DTSTART:20220426T130000Z DTEND:20220426T140000Z DTSTAMP:20260422T201546Z UID:CAvid/72 DESCRIPTION:Title: W andering domains in transcendental dynamics: topology and dynamics\nby David Marti-Pete (University of Liverpool) as part of CAvid: Complex Anal ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nFor a transcendent al entire or meromorphic function\, the Fatou set is the largest open set on which its iterates are defined and form a normal family. A wandering do main is a connected component of the Fatou set which is not eventually per iodic. The first example of a transcendental entire function with a wander ing domain was constructed by Baker in the 1970s. \n\nWandering domains\, which do not exist for rational maps\, play an important role in transcend ental dynamics and in the last decade there has been a resurgence in their interest. For example\, Bishop proved that the Julia sets of transcendent al entire functions can have Hausdorff dimension 1 by constructing a funct ion with wandering domains. \n\nWandering domains are very diverse in term s of both their topology (simply connected or multiply connected) and thei r dynamics (escaping\, oscillating or\, perhaps\, even have bounded orbit) . Recently\, Boc Thaler proved the surprising result that every bounded re gular domain such that its closure has a connected complement is the wande ring domain of some transcendental entire function. Inspired by this resul t\, together with Rempe and Waterman\, we were able to obtain wandering do mains that form Lakes of Wada. \n\nIn this talk\, I will describe the main topological and dynamical properties of wandering domains (and their boun daries) and give an overview of the current open questions.\n LOCATION:https://researchseminars.org/talk/CAvid/72/ END:VEVENT END:VCALENDAR