A generalization of the self-dual induction to every interval exchange transformation

Sébastien Ferenczi[1]

  • [1] Institut de Mathématiques de Marseille CNRS - UMR 7373 Case 907 - 163 av. de Luminy F13288 Marseille Cedex 9 (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 5, page 1947-2002
  • ISSN: 0373-0956

Abstract

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We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic and rotations Rauzy classes.

How to cite

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Ferenczi, Sébastien. "A generalization of the self-dual induction to every interval exchange transformation." Annales de l’institut Fourier 64.5 (2014): 1947-2002. <http://eudml.org/doc/275658>.

@article{Ferenczi2014,
abstract = {We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic and rotations Rauzy classes.},
affiliation = {Institut de Mathématiques de Marseille CNRS - UMR 7373 Case 907 - 163 av. de Luminy F13288 Marseille Cedex 9 (France)},
author = {Ferenczi, Sébastien},
journal = {Annales de l’institut Fourier},
keywords = {Dynamical systems; interval exchanges; symbolic dynamics; dynamical systems},
language = {eng},
number = {5},
pages = {1947-2002},
publisher = {Association des Annales de l’institut Fourier},
title = {A generalization of the self-dual induction to every interval exchange transformation},
url = {http://eudml.org/doc/275658},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Ferenczi, Sébastien
TI - A generalization of the self-dual induction to every interval exchange transformation
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 5
SP - 1947
EP - 2002
AB - We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic and rotations Rauzy classes.
LA - eng
KW - Dynamical systems; interval exchanges; symbolic dynamics; dynamical systems
UR - http://eudml.org/doc/275658
ER -

References

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