BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mauro Artigiani (Universidad del Rosario (Colombia)) DTSTART:20210617T140000Z DTEND:20210617T150000Z DTSTAMP:20260423T023017Z UID:DinAmicI/26 DESCRIPTION:Title: Double rotations and their ergodic properties\nby Mauro Artigiani (U niversidad del Rosario (Colombia)) as part of DinAmicI: Another Internet S eminar\n\n\nAbstract\nDouble rotations are the simplest subclass of interv al translation mappings. A double rotation is of finite type if its attrac tor is an interval and of infinite type if it is a Cantor set. It is easy to see that the restriction of a double rotation of finite type to its att ractor is simply a rotation. It is known due to Suzuki - Ito - Aihara and Bruin - Clark that double rotations of infinite type are defined by a subs et of zero measure in the parameter set. We introduce a new renormalizatio n procedure on double rotations\, which is reminiscent of the classical Ra uzy induction. Using this renormalization\, we prove that the set of param eters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover\, we construct a natural invariant measu re supported on these parameters and show that\, with respect to this meas ure\, almost all double rotations are uniquely ergodic. In my talk I plan to outline this proof that is based on the recent result by Fougeron for s implicial systems. I also hope to discuss briefly some challenging open qu estions and further research plans related to double rotations.\n\nThe tal k is based on a joint work with Charles Fougeron\, Pascal Hubert and Sasha Skripchenko.\n LOCATION:https://researchseminars.org/talk/DinAmicI/26/ END:VEVENT END:VCALENDAR