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SUMMARY:Alexandra Skripchenko (Higher School of Economics)
DTSTART:20210316T133000Z
DTEND:20210316T143000Z
DTSTAMP:20260423T021410Z
UID:OWNS/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/37/">Do
 uble rotations and their ergodic properties</a>\nby Alexandra Skripchenko 
 (Higher School of Economics) as part of One World Numeration seminar\n\n\n
 Abstract\nDouble rotations are the simplest subclass of interval translati
 on mappings. A double rotation is of finite type if its attractor is an in
 terval 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 attractor is si
 mply a rotation. It is known due to Suzuki - Ito - Aihara and Bruin - Clar
 k that double rotations of infinite type are defined by a subset of zero m
 easure in the parameter set. We introduce a new renormalization procedure 
 on double rotations\, which is reminiscent of the classical Rauzy inductio
 n. Using this renormalization we prove that the set of parameters which in
 duce infinite type double rotations has Hausdorff dimension strictly small
 er than 3. Moreover\, we construct a natural invariant measure supported o
 n these parameters and show that\, with respect to this measure\, almost a
 ll double rotations are uniquely ergodic. In my talk I plan to outline thi
 s proof that is based on the recent result by Ch. Fougeron for simplicial 
 systems. I also hope to discuss briefly some challenging open questions an
 d further research plans related to double rotations. \n\nThe talk is base
 d on a joint work with Mauro Artigiani\, Charles Fougeron and Pascal Huber
 t.\n
LOCATION:https://researchseminars.org/talk/OWNS/37/
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