# Generic points in the cartesian powers of the Morse dynamical system

Emmanuel Lesigne; Anthony Quas; Máté Wierdl

Bulletin de la Société Mathématique de France (2003)

- Volume: 131, Issue: 3, page 435-464
- ISSN: 0037-9484

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topLesigne, Emmanuel, Quas, Anthony, and Wierdl, Máté. "Generic points in the cartesian powers of the Morse dynamical system." Bulletin de la Société Mathématique de France 131.3 (2003): 435-464. <http://eudml.org/doc/272360>.

@article{Lesigne2003,

abstract = {The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.},

author = {Lesigne, Emmanuel, Quas, Anthony, Wierdl, Máté},

journal = {Bulletin de la Société Mathématique de France},

keywords = {topological dynamics; ergodic theory; symbolic dynamical systems; Morse sequence; odometer; joinings; generic points; weak disjointness},

language = {eng},

number = {3},

pages = {435-464},

publisher = {Société mathématique de France},

title = {Generic points in the cartesian powers of the Morse dynamical system},

url = {http://eudml.org/doc/272360},

volume = {131},

year = {2003},

}

TY - JOUR

AU - Lesigne, Emmanuel

AU - Quas, Anthony

AU - Wierdl, Máté

TI - Generic points in the cartesian powers of the Morse dynamical system

JO - Bulletin de la Société Mathématique de France

PY - 2003

PB - Société mathématique de France

VL - 131

IS - 3

SP - 435

EP - 464

AB - The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.

LA - eng

KW - topological dynamics; ergodic theory; symbolic dynamical systems; Morse sequence; odometer; joinings; generic points; weak disjointness

UR - http://eudml.org/doc/272360

ER -

## References

top- [1] H. Furstenberg – « Strict ergodicity and transformations of the torus », Amer. J. Math83 (1961), p. 573–601. Zbl0178.38404MR133429
- [2] E. Lesigne, C. Mauduit & B. Mossé – « Le théorème ergodique le long d’une suite $q$-multiplicative », Comp. Math.93 (1994), p. 49–79. Zbl0818.28006MR1286798
- [3] E. Lesigne, A. Quas, T. de la Rue & B. Rittaud – « Weak disjointness in ergodic theory », Proceedings of the Conference on Ergodic Theory and Dynamical Systems, Toruń 2000, Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland, 2001.
- [4] E. Lesigne, B. Rittaud & T. de la Rue – « Weak disjointness of measure preserving dynamical systems », to appear in Ergodic Theory & Dynamycal Systems. Available in PDF format as http://www.csi.hu/mw/Weak-Disj.TEB.2.pdf and in DVI format as http://www.csi.hu/mw/Weak-Disj.TEB.2.dvi. Zbl1083.37003
- [5] C. Mauduit – « Substitutions et ensembles normaux », Habilitation à diriger des recherches, Université Aix-Marseille II, 1989.
- [6] M. Morse – « Recurrent geodesics on a surface of negative curvature », Trans. Amer. Math. Soc.22 (1921), p. 84–100. Zbl48.0786.06MR1501161JFM48.0786.06
- [7] E. Prouhet – « Mémoire sur quelques relations entre les puissances des nombres », C. R. Acad. Sci. Paris 33 (1851), p. 225.
- [8] A. Thue – « Uber unendliche Zeichenreihen (1906), uber die gegenseitige lage gleicher teile gewisser zeichenreihen (1912) », Selected mathematical papers of Axel Thue, Universitetsforlaget, 1977. JFM39.0283.01

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