Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 
 

 

An example of PET. Computation of the Hausdorff dimension of the aperiodic set


Authors: Nicolas Bédaride and Jean-François Bertazzon
Journal: Trans. Amer. Math. Soc. 370 (2018), 357-391
MSC (2010): Primary 37A10, 37A45, 37E15
DOI: https://doi.org/10.1090/tran/6948
Published electronically: September 8, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a family of piecewise isometries. This family is similar to the ones studied by Hooper and Schwartz. We prove that a renormalization scheme exists inside this family and compute the Hausdorff dimension of the discontinuity set. The methods use some cocycles and a continued fraction algorithm.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 37A10, 37A45, 37E15

Retrieve articles in all journals with MSC (2010): 37A10, 37A45, 37E15


Additional Information

Nicolas Bédaride
Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
Email: nicolas.bedaride@univ-amu.fr

Jean-François Bertazzon
Affiliation: Lycée Notre-Dame de Sion, 231 Rue Paradis, 13006 Marseille, France
Email: jeffbertazzon@gmail.com

DOI: https://doi.org/10.1090/tran/6948
Received by editor(s): December 10, 2015
Received by editor(s) in revised form: March 29, 2016
Published electronically: September 8, 2017
Additional Notes: This work was supported by the Agence Nationale de la Recherche – ANR-10-JCJC 01010
Article copyright: © Copyright 2017 American Mathematical Society