Skip to main content
Log in

Abstract

Certain families of manifolds which support Anosov flows do not support foliations which both are expanding under a dynamical system and have quasi-isometrically embedded leaves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Baraviera and C. Bonatti. Removing zero lyapunov exponents. Ergod. Th. and Dynam. Sys., 23 (2003), 1655–1670.

    Article  MATH  MathSciNet  Google Scholar 

  2. I. Belegradek. On Mostow rigidity for variable negative curvature. Topology, 41(2) (2002), 341–361.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Brin. On dynamical coherence. Ergod. Th. and Dynam. Sys., 23 (2003), 395–401.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Brin, D. Burago and S. Ivanov. Dynamical coherence of partially hyperbolic diffeomorphisms of the 3-torus. Journal of Modern Dynamics, 3(1) (2009), 1–11.

    Article  MATH  MathSciNet  Google Scholar 

  5. K. Burns and A. Wilkinson. Dynamical coherence and center bunching. Discrete and Continuous Dynamical Systems, 22(1&2) (2008), 89–100.

    MATH  MathSciNet  Google Scholar 

  6. S. R. Fenley. Quasi-isometric folations. Topology, 31(3) (1992), 667–676.

    Article  MATH  MathSciNet  Google Scholar 

  7. É. Ghys. Codimension one Anosov flows and suspensions. In Dynamical systems, Valparaiso 1986, volume 1331 of Lecture Notes in Math., pages 59–72. Springer, Berlin (1988).

    Google Scholar 

  8. A. Hammerlindl. Quasi-isometry and plaque expansiveness. Canadian Math. Bull., 54(4) (2011), 676–679.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Hammerlindl. The dynamics of quasi-isometric foliations. Nonlinearity, 25 (2012), 1585–1599.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Hammerlindl. Leaf conjugacies on the torus. Ergodic Theory Dynam. Systems, 33(3) (2013), 896–933. Thesis, University of Toronto (2009).

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Hammerlindl. Partial hyperbolicity on 3-dimensional nilmanifolds. Discrete and Continuous Dynamical Systems, 33(8) (2013), 3641–3669.

    Article  MATH  MathSciNet  Google Scholar 

  12. Andy Hammerlindl. Polynomial global product structure. Proc. Amer. Math. Soc., 142(12) (2014), 4297–4303.

    Article  MATH  MathSciNet  Google Scholar 

  13. F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures. A survey of partially hyperbolic dynamics. “PartiallyHyperbolicDynamics, Lamnations, and Teichmüller Flow,” (eds. G. Forni, M. Lyubich, C. Pugh and M. Shub), (2007), 103–112.

  14. M. Hirsch, C. Pugh and M. Shub. Invariant Manifolds, volume 583 of Lecture Notes in Mathematics. Springer-Verlag (1977).

    Google Scholar 

  15. G. D. Mostow. Strong rigidity of locally symmetric spaces. Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo. Annals of Mathematics Studies, No. 78, (1973).

    MATH  Google Scholar 

  16. V. Oseledets. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc., 19 (1968), 197–231.

    MATH  Google Scholar 

  17. K. Parwani. On 3-manifolds that support partially hyperbolic diffeomorphisms. Nonlinearity, 23 (2010), 589–606.

    Article  MATH  MathSciNet  Google Scholar 

  18. M. Shub and A. Wilkinson. Pathological foliations and removable zero exponents. Invent. Math., 139(3) (2000), 495–508.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. R. A. Varão Filho. Absolute continuity for diffeomorphisms with non-compact center leaves. PhD thesis, IMPA (2012).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andy Hammerlindl.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hammerlindl, A. On expanding foliations. Bull Braz Math Soc, New Series 46, 407–420 (2015). https://doi.org/10.1007/s00574-015-0097-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00574-015-0097-7

Keywords

Mathematical subject classification

Navigation