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Mauro Artigiani (Universidad del Rosario, Colombia)

June 17 @ 4:00 pm - 5:00 pm CEST

Speaker: Mauro Artigiani  (Universidad del Rosario, Colombia)

Title: Double rotations and their ergodic properties

Abstract: Double rotations are the simplest subclass of interval translation mappings. A double rotation is of finite type if its attractor 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 attractor 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 subset of zero measure in the parameter set. We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization, we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, 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 simplicial systems. I also hope to discuss briefly some challenging open questions and further research plans related to double rotations.
The talk is based on joint work with Charles Fougeron, Pascal Hubert and Sasha Skripchenko.

NOTE: The seminar will be streamed live on our YouTube channel then saved there. If you ask questions, with your video feed on or off, you agree to the use of your image/spoken words for said purpose.

Details

Date:
June 17
Time:
4:00 pm - 5:00 pm CEST
Event Category:

Venue

Seminar is over: watch it on our YouTube channel (link below)
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Organizer

DAI Seminar Committee
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The Community of Italian Dynamicists