BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Brandenbursky (Ben-Gurion University) DTSTART:20220427T111000Z DTEND:20220427T120000Z DTSTAMP:20260423T005735Z UID:GDS/54 DESCRIPTION:Title: C^0 -gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of s urfaces\nby Michael Brandenbursky (Ben-Gurion University) as part of G eometry and Dynamics seminar\n\n\nAbstract\nLet Σ be a surface equipped w ith an area form. There is a long standing open \nquestion by Katok\, whic h\, in particular\, asks whether every entropy-zero \nHamiltonian diffeomo rphism of a surface lies in the C^0-closure of the set \nof integrable dif feomorphisms. A slightly weaker version of this question \nasks: ``Does ev ery entropy-zero Hamiltonian diffeomorphism of a surface lie \nin the C^0- closure of the set of autonomous diffeomorphisms?'' In this talk \nI will answer in negative the later question. In particular\, I will show that \n on a surface Σ the set of autonomous Hamiltonian diffeomorphisms is not \ nC^0-dense in the set of entropy-zero Hamiltonians. Explicitly constructed \nexamples of such Hamiltonians cannot be approximated by autonomous \ndi ffeomorphisms. (Joint with M. Khanevsky).\n LOCATION:https://researchseminars.org/talk/GDS/54/ END:VEVENT END:VCALENDAR