BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luna Lomonaco (IMPA) DTSTART:20200813T190000Z DTEND:20200813T200000Z DTSTAMP:20260423T021247Z UID:UFPB/3 DESCRIPTION:Title: The Mandelbrot set and its Satellite copies\nby Luna Lomonaco (IMPA) as p art of Seminários de Matemática da UFPB\n\n\nAbstract\nFor a polynomial on the Riemann sphere\, infinity is a (super) attracting fixed point\, and the filled Julia set is the set of points with bounded orbit. Consider th e quadratic family P_c(z)=z^2+c. The Mandelbrot set M is the set of param eters c such that the filled Julia set of P_c is connected. Douady and Hub bard proved the existence of homeomorphic copies of M inside of M\, which can be primitive (roughly speaking the ones with a cusp) or a satellite (w ithout a cusp). Lyubich proved that the primitive copies of M are quasicon formally homeomorphic to M\, and that the satellite ones are quasiconforma lly homeomorphic to M outside any small neighbourhood of the root. The sat ellite copies are not quasiconformally homeomorphic to M\, but are they mu tually quasiconformally homeomorphic? In a joint work with C. Petersen we prove that this question has in general a negative answer\n LOCATION:https://researchseminars.org/talk/UFPB/3/ END:VEVENT END:VCALENDAR