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Original Articles

Interval exchange transformations over algebraic number fields: the cubic Arnoux–Yoccoz model

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Pages 73-106 | Received 10 May 2006, Accepted 01 Sep 2006, Published online: 06 Mar 2007

References

  • Boshernitzan , MD and Carroll , CR . 1997 . An extension of Lagrange's theorem. . Journal d'Analyse Mathématique , 72 : 21 – 44 .
  • Vershik , AM . 1985 . A theorem on the Markov periodical approximation in ergodic theory. . Journal of Soviet Mathematics , 28 : 667 – 674 .
  • Rauzy , G . 1982 . Nombre Algébriques et Substitutions. . Bulletin de la Société Mathématique de France , 110 : 147 – 178 .
  • Pytheas Fogg , N . 2002 . Substitutions in Dynamics, Arithmetics and Combinatorics , Berlin : Springer-Verlag .
  • Akiyama , S . 1999 . “ Self-affine tiling and Pisot numeration system ” . In Number Theory and its Applications , Edited by: Kanemitzu , S and Gÿory , K . 7 – 17 . Dordrecht : Kluwer Academic Publishers .
  • Ito , S and Kimura , M . 1991 . On Rauzy fractal. . Japan Journal of Industrial and Applied Mathematics , 8 : 461 – 486 .
  • Messaoudi , A . 2000 . Frontière du fractal de Rauzy et système de numération complexe. . Acta Arithmetica , 95 : 195 – 224 .
  • Veech , W . 1984 . The metric theory of interval exchange transformations. III. The Sah–Arnoux–Fathi invariant, . American Journal of Mathematics , 106 ( 6 ) : 1389 – 1422 .
  • Arnoux , P and Rauzy , G . 1991 . Représentation géométrique de suites de complexité 2n+1. (French) [Geometric representation of sequences of complexity 2n+1]. . Bulletin de la Société Mathématique de France , 119 ( 2 ) : 199 – 215 .
  • Arnoux , P and Yoccoz , J . 1981 . Construction de diffeomorphismes pseudo-Anosov. . Comptes Rendus de l'Académie des Sciences Paris , 292 : 75 – 78 .
  • Kouptsov , KL , Lowenstein , JH and Vivaldi , F . 2002 . Quadratic rational rotations of the torus and dual lattice maps. . Nonlinearity , 15 : 1795 – 1482 .
  • Lowenstein , JH , Poggiaspalla , G and Vivaldi , F . 2005 . Sticky orbits in a kicked-oscillator model. . Dynamical Systems , 20 : 413 – 451 .
  • Holton , C and Zamboni , L . 1998 . Geometric realizations of substitutions. . Bulletin de la Société Mathématique de France , 126 ( 2 ) : 149 – 179 .
  • Canterini , V and Siegel , A . 2001 . Automate des préfixes-suffixes associé à une substitution primitive (in French. English summary) [Prefix-suffix automaton associated with a primitive substitution]. . Journal de Théorie des Nombres Bordeaux , 13 ( 2 ) : 353 – 369 .
  • Lowenstein , JH , Kouptsov , KL and Vivaldi , F . 2004 . Recursive tiling and geometry of piecewise rotations by π/7. . Nonlinearity , 17 : 1 – 25 .

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