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Symbolic Dynamics of a Piecewise Rotation: Case of the Non Symmetric Bijective Maps

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Abstract

We consider a specific piecewise rotation of the plane that is continuous on two half-planes, as studied by some authors like Boshernitzan, Goetz and Quas. If the angle belongs to the set \(\{\frac{\pi }{2},\frac{2\pi }{3},\frac{\pi }{4}\}\), we give a complete description of the symbolic dynamics of this map in the non symmetric bijective case.

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References

  1. Bédaride, N., Cassaigne, J.: Outer billiard outside regular polygons. J. Lond. Math. Soc. (2) 84(2), 303–324 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bédaride, N., Kaboré, I.: Symbolic dynamics of a piecewise rotation: symmetric case. Arxiv preprint (2015)

  3. Boshernitzan, M., Goetz, A.: A dichotomy for a two-parameter piecewise rotation. Ergod. Theory Dyn. Syst. 23(3), 759–770 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fogg, N.P.: Substitutions in dynamics, arithmetics and combinatorics. In: Berthé, V., Ferenczi, S., Mauduit, C., Siegel, A. (eds.) Volume 1794 of Lecture Notes in Mathematics. Springer, Berlin (2002)

    Google Scholar 

  5. Goetz, A., Quas, A.: Global properties of a family of piecewise isometries. Ergod. Theory Dyn. Syst. 29(2), 545–568 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. CNRS, Centrale Marseille, I2M, UMR 7373, Aix Marseille Université, 13453, Marseille, France

    Nicolas Bédaride

  2. Université Nazi Boni UFR Sciences et Techniques, 01 PB 1091, Bobo-Dioulasso, Burkina Faso

    Idrissa Kaboré

Authors
  1. Nicolas Bédaride
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  2. Idrissa Kaboré
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Corresponding author

Correspondence to Nicolas Bédaride.

Additional information

Idrissa Kaboré would like to thanks EMS-Simons for Africa for its grant.

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Bédaride, N., Kaboré, I. Symbolic Dynamics of a Piecewise Rotation: Case of the Non Symmetric Bijective Maps. Qual. Theory Dyn. Syst. 17, 651–664 (2018). https://doi.org/10.1007/s12346-017-0267-7

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  • DOI: https://doi.org/10.1007/s12346-017-0267-7

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