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

• Autorzy: Fel'shtyn A. L.
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1991
• Tom: 62
• Numer: 1
• Strony: 153-166

Daty

wydano

1991

otrzymano

1989-09-05

Twórcy

autor

Fel'shtyn A. L.

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

Bibliografia

• [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.