Symmetric interval identification systems of order three

Alexandra Skripchenko

doi:10.3934/dcds.2012.32.643

Article Contents

2012, Volume 32, Issue 2: 643-656. Doi: 10.3934/dcds.2012.32.643

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Symmetric interval identification systems of order three

Alexandra Skripchenko^1,

1.
Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991

Received: October 31, 2010

Revised: May 31, 2011

Published: January 2012

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Abstract

In the present paper we study symmetric interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order 3 after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of symmetric interval identification system of thin type.

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Mathematics Subject Classification: Primary: 37E05, 37E25; Secondary: 57M99.

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