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Remarks on the horocycle flows for foliations by hyperbolic surfaces


Author: Shigenori Matsumoto
Journal: Proc. Amer. Math. Soc. 145 (2017), 355-362
MSC (2010): Primary 53C12; Secondary 57R30, 20H10
DOI: https://doi.org/10.1090/proc/13184
Published electronically: June 30, 2016
MathSciNet review: 3565386
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Abstract: We show that the horocycle flow associated with a foliation on a compact manifold by hyperbolic surfaces is minimal under certain conditions.


References [Enhancements On Off] (What's this?)

  • [1] Fernando Alcalde Cuesta and Françoise Dal'Bo, Remarks on the dynamics of the horocycle flow for homogeneous foliations by hyperbolic surfaces, Expo. Math. 33 (2015), no. 4, 431-451. MR 3431475, https://doi.org/10.1016/j.exmath.2015.07.006
  • [2] F. Alcalde, F.Dal'bo, M. Martínez, and A. Verjovsky, Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology, Discrete and Continuous Dynamical Systems, 36 (2016) 4619-4635.
  • [3] Gustav A. Hedlund, Fuchsian groups and transitive horocycles, Duke Math. J. 2 (1936), no. 3, 530-542. MR 1545946, https://doi.org/10.1215/S0012-7094-36-00246-6
  • [4] M. Martínez, S. Matsumoto, and A. Verjovsky, Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem, Journal of Modern Dynamics, 10 (2016) 113-134.
  • [5] Harold Rosenberg, Foliations by planes, Topology 7 (1968), 131-138. MR 0228011
  • [6] Dennis Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 465-496. MR 624833
  • [7] W. Thurston, Foliations of 3-manifolds which are circle bundles, Thesis Berkeley 1971.

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Additional Information

Shigenori Matsumoto
Affiliation: Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda, Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan
Email: matsumo@math.cst.nihon-u.ac.jp

DOI: https://doi.org/10.1090/proc/13184
Keywords: Foliations, hyperbolic surfaces, horocycle flows, minimal sets.
Received by editor(s): August 7, 2015
Received by editor(s) in revised form: March 6, 2016
Published electronically: June 30, 2016
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C) No. 25400096.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society

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