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Weakly mixing billiards

Part of the Lecture Notes in Mathematics book series (LNM,volume 1345)

Keywords

  • Invariant Measure
  • Linear Flow
  • Interval Exchange Transformation
  • Billiard Table
  • Liouville Measure

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References

  1. E. Gutkin, Billiards on almost integrable polyhedral surfaces, Erg. Th. and Dyn. Syst., 4, N4(1984), 569–584.

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  2. P. R. Halmos, Lectures on Ergodic Theory, Tokyo, 1956.

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  3. A. Katok, Constructions in Ergodic Theory, Part 1, preprint, to appear in Birkhauser, Progress in Math.

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  4. A. Katok, Ergodicity of generic irrational billiards, Abstracts from workshop on 2-manifolds and Geometry, Oct. 1984, MSRI, Jan. 1986.

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  5. A. Katok, The growth rate for the number of singular and periodic orbits for a polygonal billiard, preprint, 1984.

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  6. A. Katok, Interval exchange transformations and some special flows are not mixing, Israel J. of Math. 35 (1980), 301–310.

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  7. S. Kerckhoff, H. Masur, J. Smillie, Ergodicity of billiard lows and quadratic differentials, to appear in Ann. of Math.

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© 1988 Springer-Verlag

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Gutkin, E., Katok, A. (1988). Weakly mixing billiards. In: Gomez-Mont, X., Seade, J.A., Verjovski, A. (eds) Holomorphic Dynamics. Lecture Notes in Mathematics, vol 1345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081401

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  • DOI: https://doi.org/10.1007/BFb0081401

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50226-5

  • Online ISBN: 978-3-540-45957-6

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