Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize

Stefano Marmi

doi:10.3934/jmd.2022006

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2022, Volume 18: 131-147. Doi: 10.3934/jmd.2022006 open access

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Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize (Brin prize article)

Stefano Marmi

Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Received: November 21, 2021

Revised: February 06, 2022

Published: April 2022

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Abstract

We present some works of Corinna Ulcigrai closely related to Diophantine approximations and generalizing classical notions to the context of interval exchange maps, translation surfaces and Teichmüller dynamics.

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Mathematics Subject Classification: Primary: 11J06; Secondary: 11J70, 37E05, 37E20.

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Figure 1. The Brjuno function $ B(\alpha) $

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Figure 2. Rauzy diagram for 2 and 3 intervals

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Figure 3. Rauzy diagrams for 4 intervals and genus 2

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Figure 4. Rauzy diagram for $ d = 6 $ (using the same set of notations [46]). This figure is an extract of the Master thesis of Corinna Ulcigrai, Pisa, 2002

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