Skip to main content

Periodic points and lefschetz numbers

  • 672 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 668)

Keywords

  • Zeta Function
  • Periodic Point
  • Euler Characteristic
  • Homotopy Class
  • Topological Entropy

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.

Bibliography

  1. R. Bowen, Topological entropy and Axiom A, Proc. Sympos. Pure Math. 14, Amer. Math. Soc., Providence, R.I., 23–42.

    Google Scholar 

  2. J. Franks, A reduced zeta function for diffeomorphisms, to appear in Amer. J. of Math.

    Google Scholar 

  3. J. Franks, Some smooth maps with infinitely many hyperbolic periodic points, to appear in Trans. Amer. Math. Soc.

    Google Scholar 

  4. J. Guckenheimer, Axiom A and no-cycles imply ς(f) rational, Bull. Amer. Math. Soc. 76(1970), 592–594.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. A. Manning, Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3(1971), 215–220.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. C. Narasimhan, The periodic behavior of Morse-Smale diffeomorphisms on compact surfaces, Thesis, Northwestern University, 1977.

    Google Scholar 

  7. J. Neuberger, An iterative method for solving nonlinear partial differential equations, Advances in Math. 19(1976), 245–265.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. M. Shub and D. Sullivan, Homology theory and dynamical systems, Topology 14(1975), 109–132.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73(1967), 747–817.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. R. Williams, The zeta function of an attractor, Conference on Topology of Manifolds (Michigan State 1967), Prindle, Weber and Schmidt (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this chapter

Cite this chapter

Batterson, S. (1978). Periodic points and lefschetz numbers. In: Markley, N.G., Martin, J.C., Perrizo, W. (eds) The Structure of Attractors in Dynamical Systems. Lecture Notes in Mathematics, vol 668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101776

Download citation

  • DOI: https://doi.org/10.1007/BFb0101776

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08925-4

  • Online ISBN: 978-3-540-35751-3

  • eBook Packages: Springer Book Archive