A Reduced Zeta Function for Diffeomorphisms
Publications des séminaires de mathématiques et informatique de Rennes, International Conference on Dynamical Systems in Mathematical Physics, no. S4 (1975), article no. 8, 39 p. 
@article{PSMIR_1975___S4_A8_0,
     author = {Franks, John M.},
     title = {A {Reduced} {Zeta} {Function} for {Diffeomorphisms}},
     journal = {Publications des s\'eminaires de math\'ematiques et informatique de Rennes},
     eid = {8},
     pages = {1--39},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {S4},
     year = {1975},
     language = {en},
     url = {http://www.numdam.org/item/PSMIR_1975___S4_A8_0/}
}
TY  - JOUR
AU  - Franks, John M.
TI  - A Reduced Zeta Function for Diffeomorphisms
JO  - Publications des séminaires de mathématiques et informatique de Rennes
PY  - 1975
SP  - 1
EP  - 39
IS  - S4
PB  - Département de Mathématiques et Informatique, Université de Rennes
UR  - http://www.numdam.org/item/PSMIR_1975___S4_A8_0/
LA  - en
ID  - PSMIR_1975___S4_A8_0
ER  - 
%0 Journal Article
%A Franks, John M.
%T A Reduced Zeta Function for Diffeomorphisms
%J Publications des séminaires de mathématiques et informatique de Rennes
%D 1975
%P 1-39
%N S4
%I Département de Mathématiques et Informatique, Université de Rennes
%U http://www.numdam.org/item/PSMIR_1975___S4_A8_0/
%G en
%F PSMIR_1975___S4_A8_0
Franks, John M. A Reduced Zeta Function for Diffeomorphisms. Publications des séminaires de mathématiques et informatique de Rennes, International Conference on Dynamical Systems in Mathematical Physics, no. S4 (1975), article  no. 8, 39 p. http://www.numdam.org/item/PSMIR_1975___S4_A8_0/

1. M. Artin and B. Mazur, On Periodic Points, Annals of Math. (2) 81(1965), 82-99. | MR | Zbl

2. R. Bowen, Topological Entropy and Axiom A, Proc. Sympos. Pure Math. 14, Amer. Math. Soc., Providence, R. I., 23-42. | MR | Zbl

3. A. Dold, Fixed Point Index and Fixed Point Theorem for Euclidean Neighborhood Retracts, Topology 4(1965), 1-8. | MR | Zbl

4. J. Franks, Morse Inequalities for Zeta Functions, to appear In Annals of Math. | MR | Zbl

5. J. Guckenheimer, Axiom A and no cycles Imply ζ(f) rational, Bull. Amer. Math. Soc. 76(1970), 592-594. | MR | Zbl

6. M. Hirsch and C. Pugh, Stable Manifolds and Hyperbolic Sets, Proc. Symp. Pure Math. 14(1970), 133-163. | MR | Zbl

7. S. Lang, Algebra, Addison-Wesley, 1965. | MR | Zbl

8. A. Manning, Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3(1971), 215-220. | MR | Zbl

9. M. Shub, Structurally Stable Diffeomorphisms are Dense, Bull. A.M.S. 78(1972), 817. | MR | Zbl

10. M. Shub and R. Williams, Entropy and Stability, to appear. | MR | Zbl

11. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73(1967), 747-817. | MR | Zbl

12. S. Smale, The Ω-stability Theorem, Proc Symp. Pure Math., 14(1970), 289-297. | MR | Zbl

13. S. Smale, Stability and Isotopy in Discrete Dynamical Systems, Proceedings of the Symposium on Dynamical Systems, Salvador, Brazil, Academic Press, 1971. | MR | Zbl

14. R. F. Williams, The Zeta function of an attractor, Conference on the Topology of Manifolds (Michigan State 1967), Prindle, Weber and Schmidt, 1968. | MR | Zbl

15. R. F. Williams, Classification of subshifts of finite type, Annals of Math.98(1973), 120-153. | MR | Zbl

16. E. C. Zeeman, C° Density of Stable Diffeomorphisms and Flows, University of Southampton Colloquium on Smooth Dynamical Systems, 1972 (mimeographed notes).