\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Symmetric interval identification systems of order three

Abstract Related Papers Cited by
  • In the present paper we study symmetric interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order 3 after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of symmetric interval identification system of thin type.
    Mathematics Subject Classification: Primary: 37E05, 37E25; Secondary: 57M99.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    M. Bestvina and M. Feighn, Stable actions of groups on real trees, Invent. Math., 121 (1995), 287-321.

    [2]

    M. Bestvina, $\mathbbR$-trees in topology, geometry, and group theory, in "Handbook of Geometric Topology," North-Holland, Amsterdam, (2002), 55-91.

    [3]

    M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergodic Theory and Dynamical Systems, 15 (1995), 821-832.doi: 10.1017/S0143385700009652.

    [4]

    H. Bruin and S. Troubetzkoy, The Gauss Map on a class of interval translation mappings, Israel J. Math, 137 (2003), 125-148.doi: 10.1007/BF02785958.

    [5]

    I. Dynnikov, Interval identification systems and plane sections of 3-periodic surfaces, Proceedings of the Steklov Institute of Mathematics, 263 (2008), 65-77.doi: 10.1134/S0081543808040068.

    [6]

    I. Dynnikov and B. Wiest, On the complexity of braids, J. Eur. Math. Soc., 9 (2007), 801-840.doi: 10.4171/JEMS/98.

    [7]

    I. Dynnikov, Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples, in "Solitons, Geometry, and Topology: On the Crossroad" AMS Transl., Ser. 2, 179, Amer. Math. Soc., Providence, RI, (1997), 45-73.

    [8]

    D. Gaboriau, Dynamique des systèmes d'isométries: Sur les bouts des orbits, Invent. Math., 126 (1996), 297-318.doi: 10.1007/s002220050101.

    [9]

    G. Levitt, La dynamique des pseudogroupes de rotations, Invent. Math., 113 (1993), 633-670.doi: 10.1007/BF01244321.

    [10]

    S. P. Novikov, The Hamiltonian formalism and many-valued analogue of Morse theory, Usp. Mat. Nauk, 37 (1982), 3-49.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(132) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return