BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anna Miriam Benini (Università di Parma) DTSTART:20220118T140000Z DTEND:20220118T150000Z DTSTAMP:20260422T201702Z UID:CAvid/62 DESCRIPTION:Title: B ifurcations arise when there is a drastic change in the solutions of some equation depending on a parameter\, as the parameter\nby Anna Miriam B enini (Università di Parma) as part of CAvid: Complex Analysis video semi nar\n\nLecture held in N/A.\n\nAbstract\nBifurcations arise when there is a drastic change in the solutions of some equation depending on a paramete r\, as the parameter varies.\nIn this talk we study bifurcations in holomo rphic families of meromorphic maps with finitely many singular values. Th e equation(s) that we will study are the equations defining periodic point s of period n. Such equations are crucial in complex dynamics because the Julia set (the set on which the dynamics is chaotic) is the closure of rep elling periodic points. The celebrated results by Mane-Sad-Sullivan for fa milies of rational maps (and independently by Lyubich\, and by Levin for p olynomials) show that in a set of parameters where no bifurcations of pe riodic points occur\, the Julia set stays almost the same and so does the dynamics\; precisely speaking\, all maps are topologically conjugate in s uch set. Moreover\, they establish a precise correlation between bifurca tions of periodic points and a change of behaviour in the orbits of singul ar values.\nThe key new feature that appears for families of meromorphic maps is that periodic points can disappear at infinity at specific param eters\, creating a new type of bifurcations. Our work connects this new ty pe of bifurcations with change of behaviour in singular orbits\, to establ ish Mane-Sad-Sullivan's Theorem for meromorphic maps.\nThis is joint wor k with Matthieu Astorg and Nùria Fagella.\n LOCATION:https://researchseminars.org/talk/CAvid/62/ END:VEVENT END:VCALENDAR