Skip to main content
SpringerLink
Log in

New zeta functions for dynamical systems and Nielsen fixed point theory

  • Chapter
  • First Online:
Topology and Geometry — Rohlin Seminar

Part of the book series: Lecture Notes in Mathematics ((2179,volume 1346))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fel’shtyn A.L. New zeta function in the dynamic. Tenth International conference on nonlinear oscilliations. Abstracts of papers, Varna, NRB, 1984, 208.

    Google Scholar 

  2. Pilijugina V.B., Fel’shtyn A.L. The Nielsen zeta function. Funk. anal. i priloz., 1985, v.19, N 4, 61–67.

    MathSciNet  Google Scholar 

  3. Artin M., Mazur B. On periodic points. Annals of Math., 1965, v.81, N 1, 82–99.

    Article  MathSciNet  MATH  Google Scholar 

  4. Smale S. Differentiable dynamical systems. Bull.Amer.Math.Soc., 1967, v.73, 747–817.

    Article  MathSciNet  MATH  Google Scholar 

  5. Franks J. Homology and dynamical systems. Regional Conf. Ser.Math., 1982, N 49, 1–120.

    Google Scholar 

  6. Fried D. Periodic points and twisted coefficients.-Lect.Notes Math., 1983, v.1007, 261–293.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Weil. Numbers of Solution of equations in finite fields.-Bull. Amer. Math. Soc., 1949, v.55, 497–508.

    Article  MathSciNet  MATH  Google Scholar 

  8. Manning A. Axiom A diffeomorphism have rational zeta function.-Bull. London Math. Soc., 1971, N 3, 215–220.

    Google Scholar 

  9. Bowen R., O.E.Lanford III. Zeta functions of restrictions of the Shift transformation.-Proc. of the Global Anal., 1968, 43–49.

    Google Scholar 

  10. Hirsch G. Détermination d’un nombre minimum de points fixed pour certaines representations.-Bull. Sci. Math., 1940, v.40, 45–55.

    MATH  Google Scholar 

  11. Wecken F. Fixpunktklassen I. Math. Ann., 1941, v.117, 659–671.

    MathSciNet  MATH  Google Scholar 

  12. Boju Jang. Nielsen fixed point theory.-Contemporary Math., 1983, v.14, 1–108.

    Article  MathSciNet  Google Scholar 

  13. Ivanov N.V. Entropy and the Nielsen numbers.-Sov. Math. Dokl., 1982, N 2, v.265, 284–286.

    MathSciNet  Google Scholar 

  14. Conze J.P. Points periodiques et entropic topologique. C.R.Acad. Sc., t.267, 1968, 149–152.

    MathSciNet  MATH  Google Scholar 

  15. Shub M., Sullivan D. Homology theory and Dynamical Systems.-Topology, 1975, v.14, 109–132.

    Article  MathSciNet  MATH  Google Scholar 

  16. Bowen R. Topological Entropy and Axiom a., Global Analysis, Proc. Symp. in Pure Math., 1970, v.14, 23–41.

    Article  MathSciNet  Google Scholar 

  17. Thurston W.P. On the geometry and dynamics of diffeomorphisms of surface.-Preprint 1977.

    Google Scholar 

  18. Brooks R., Brown R.F., Pak J., Taylor D.H. Nielsen numbers of maps of tori.-Proc. Amer.Math.Soc., 1975, v.52, 398–400.

    Article  MathSciNet  MATH  Google Scholar 

  19. Shub M. Endomorphisms of compact differentiable manifolds.-Amer. J.Math., 1969, v.91, 175–179.

    Article  MathSciNet  MATH  Google Scholar 

  20. Thurston W.P. Three dimensional manifolds, Kleian groups and hyperbolic geometry. Bull.Amer.Math.Soc., 1982, v.6, 357–381.

    Article  MathSciNet  MATH  Google Scholar 

  21. Nielsen J. Untersuchungen zur Topology der geschlossenen zweiseitigen Flächen.-Acta Math., 1927, v.50, 189–348.

    Article  MathSciNet  MATH  Google Scholar 

  22. Ruelle D. An inequality for the entropy of differentiable maps. Bol.Soc.Bras.Mat., 1978, v.9, 83–88.

    Article  MathSciNet  MATH  Google Scholar 

  23. Krzyzewski K. On an estimation of topological entropy. Preprint.

    Google Scholar 

  24. Katok S. The estimation from above for the topological entropy of a diffeomorphism. Preprint.

    Google Scholar 

  25. Przytycki F. An upper estimation for topological entropy of diffeomorphisms. Inventiones math., 1980, v.59, 205–213.

    Article  MathSciNet  MATH  Google Scholar 

  26. Handel M., Thurston W.P. New Proofs of some results of Nielsen. Advances in math., 1985, v.56, 173–191.

    Article  MathSciNet  MATH  Google Scholar 

  27. Fathi A., Shub M. Some dynamics of pseudo-Anosov diffeomorphisms. Asterisque, 1979, N 66–67, 181–207.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Leningrad Technology Institute, Russia

    A. L. Fel’shtyn

Authors
  1. A. L. Fel’shtyn
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Oleg Yanovich Viro Anatoly Moiseevich Vershik

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this chapter

Cite this chapter

Fel’shtyn, A.L. (1988). New zeta functions for dynamical systems and Nielsen fixed point theory. In: Viro, O.Y., Vershik, A.M. (eds) Topology and Geometry — Rohlin Seminar. Lecture Notes in Mathematics, vol 1346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082770

Download citation

  • DOI: https://doi.org/10.1007/BFb0082770

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50237-1

  • Online ISBN: 978-3-540-45958-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation