Skip to main content

Geodesic flow on the two-sphere part II: Ergodicity

Part of the Lecture Notes in Mathematics book series (LNM,volume 1342)

Keywords

  • Universal Cover
  • Boundary Component
  • Absolute Continuity
  • Geodesic Flow
  • Markov Partition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.P. DoCarmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.

    Google Scholar 

  2. L.A. Bunimovich and Ya.G. Sinai, Markov partitions for dispersed billiards, Commun. Math. Phys. 78(1980), 247–280.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. V.J. Donnay, Geodesic flow on the two-sphere, Part I: Positive measure entropy, to appear in Ergodic Theory and Dynamical Systems.

    Google Scholar 

  4. A. Manning, Curvature bounds for the entropy of the geodesic flow on a surface, J. London Math. Soc. 24(1981), 351–357.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Ya.B. Pesin, Lyapunov characteristic exponents and smooth ergodic theory, Russ. Math. Surveys 32(1977), 55–114.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. K. Peterson, Ergodic Theory, Cambridge University Press, 1983.

    Google Scholar 

  7. M. Ratner, The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math. 16(1973), 181–197.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Ya.G. Sinai, The central limit theorem for geodesic flows on manifolds of constant negative curvature, Soviet Math. Dokl. 1(1960), 938–987.

    MathSciNet  MATH  Google Scholar 

  9. Ya.G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Uspeki Mat. Nauk. 25(1970), 141–192; Russ. Math. Surv. 25(1970), 137–189.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Donnay, V.J. (1988). Geodesic flow on the two-sphere part II: Ergodicity. In: Alexander, J.C. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082827

Download citation

  • DOI: https://doi.org/10.1007/BFb0082827

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50174-9

  • Online ISBN: 978-3-540-45946-0

  • eBook Packages: Springer Book Archive