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Journal Articles Ergodic Theory and Dynamical Systems Year : 2017

Return words of linear involutions and fundamental groups

Abstract

We investigate the shifts associated with natural codings of linear in-volutions. We deduce from the geometric representation of linear invo-lutions as Poincaré maps of measured foliations a suitable definition of return words which yields that the set of return words to a given word is a symmetric basis of the free group on the underlying alphabet A. The set of return words with respect to a subgroup of finite index G of the free group on A is also proved to be a symmetric basis of G.
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Dates and versions

hal-01367712 , version 1 (16-09-2016)

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Valérie Berthé, Vincent Delecroix, Francesco Dolce, Dominique Perrin, Christophe Reutenauer, et al.. Return words of linear involutions and fundamental groups. Ergodic Theory and Dynamical Systems, 2017, 37 (3), pp.693-715. ⟨10.1017/etds.2015.74⟩. ⟨hal-01367712⟩
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