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Title

The Reidemeister zeta function and the computation of the Nielsen zeta function

Authors 1

Affiliations

  1. Department of Mathematics, Leningrad Technology Institute, Moskovskiĭ Prosp. 26, Leningrad 198013, U.S.S.R.

Bibliography

  1. A. L. Fel'shtyn, New zeta function in dynamics, in: Tenth Internat. Conf. on Nonlinear Oscillations, Varna, Abstracts of papers, Bulgar. Acad. Sci., 1984, 208.
  2. A. L. Fel'shtyn, A new zeta-function in Nielsen theory and the universal product formula for dynamic zeta-functions, Funktsional. Anal. i Prilozhen. 21 (2) (1987), 90-91 (in Russian); English transl.: Functional Anal. Appl. 21 (1987), 168-170.
  3. A. L. Fel'shtyn, Zeta functions in Nielsen theory, Funktsional. Anal. i Prilozhen. 22 (1) (1988), 87-88 (in Russian); English transl.: Functional Anal. Appl. 22 (1988), 76-77.
  4. A. L. Fel'shtyn, New zeta functions for dynamical systems and Nielsen fixed point theory, in: Lecture Notes in Math. 1346, Springer, 1988, 33-55.
  5. A. L. Fel'shtyn, Dynamical zeta-function and the Nielsen theory, in: Baku Internat. Topological Conf., Abstracts of papers, Akad. Nauk SSSR, 1988, 311.
  6. A. L. Fel'shtyn, The Reidemeister and the Nielsen zeta functions, in: Proc. Baku Internat. Topological Conf., to appear.
  7. P. R. Heath, Product formulae for Nielsen numbers of fibre maps, Pacific J. Math. 117 (2) (1985), 267-289.
  8. N. V. Ivanov, Entropy and the Nielsen numbers, Dokl. Akad. Nauk SSSR 265 (2) (1982), 284-287 (in Russian); English transl.: Soviet Math. Dokl. 26 (1982), 63-66.
  9. B. Jiang, Nielsen Fixed Point Theory, Contemp. Math. 14, Birkhäuser, 1983.
  10. S. Lefschetz, Continuous transformations of manifolds, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 90-93.
  11. J. Nielsen, Untersuchungen zur Topologie des geschlossenen zweiseitigen Fläche, Acta Math. 50 (1927), 189-358.
  12. V. B. Pilyugina and A. L. Fel'shtyn, The Nielsen zeta function, Funktsional. Anal. i Prilozhen. 19 (4) (1985), 61-67 (in Russian); English transl.: Functional. Anal. Appl. 19 (1985), 300-305.
  13. K. Reidemeister, Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936), 586-593.
  14. M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-179.
  15. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817.
  16. W. Thurston, Three dimensional manifolds, kleinian groups, and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (3) (1982), 357-381.
  17. A. Weil, Numbers of solutions of equations in finite fields, ibid. 55 (1949), 497-508.
Colloquium Mathematicum
1991/62/1
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Pages:
153-166
Main language of publication
English
Received
1989-09-05
Published
1991
Exact and natural sciences