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Continued Fractions, Interval Exchanges and Applications to Geometry

Interval identification systems of order 3

speaker: Alexandra Skripchenko (National Research University, Higher School of Economics, Moscow, Russia)

abstract: The notion of interval identification systems (IIS) is a natural generalization of interval exchange transformations and interval translation mappings.

We are interested in particular case of such systems - symmetric IIS of order 3 due to some interesting application to 3-dimensional topology.

We define a Rauzy induction for these systems and prove a renormalization theorem which provides us with a Markov map and a fractal in original parameter space. We are interested in ergodic properties of corresponding dynamical system and in Lebesgue measure of this fractal.

timetable:
Tue 11 Jun, 16:30 - 16:55, Aula Dini
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