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  • Ergodic Theory and Dynamical Systems, Volume 4, Issue 4
  • December 1984, pp. 569-584

Billiards on almost integrable polyhedral surfaces

  • E. Gutkin (a1)
  • DOI:
  • Published online: 01 September 2008

The phase space of the geodesic flow on an almost integrable polyhedral surface is foliated into a one-parameter family of invariant surfaces. The flow on a typical invariant surface is minimal. We associate with an almost integrable polyhedral surface its holonomy group which is a subgroup of the group of motions of the Euclidean plane. We show that if the holonomy group is discrete then the flow on an invariant surface is ergodic if and only if it is minimal.

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[3]R. H. Fox & R. B. Kershner . Concerning the transitive properties of geodesies on a rationalpolyhedron. Duke Math. J. 2 (1936), 147150.

[5]H. Masur . Interval exchange transformations and measured foliations. Ann. Math. 115 (1982), 169200.

[10]P. Stäckel . Geodatische Linien auf Polyederflächen. Rend. Circ. Mat Palermo 22 (1906), 141151.

[12]W. A. Veech . Gauss measures for transformations on the space of interval exchange maps. Ann.Math. 115 (1982), 201242.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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