An extension of the Artin-Mazur theorem

Annals of Mathematics

Volumn 150, Issue 2, 1999, Pages 729-741

  Kaloshin, Vadim Yu ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033235416     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121093     Document Type: Article

References (27)

1. M. ARTIN and B. MAZUR, On periodic orbits, Ann. of Math. 81 (1965), 82-99.
2. V. BALADI, Dynamical zeta functions, in Real and Complex Dynamical Systems (Hillerød, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 464, Kluwer Acad. Publ., Dordrecht, 1995.
3. C. BONATTI and L. DIAZ, Connexions hétéroclines et généricité d'une infinité de puits et de sources, Ann. Sci. École Norm. Sup (4) 32 (1999), 135-150.
4. R. BOWEN, Rufus entropy and the fundamental group. The structure of attractors in dynamical systems (Proc. Conf., North Dakota State Univ., Fargo, ND, 1977), 21-29, Lectures Notes in Math. 668, Springer-Verlag, New York, 1978.
5. N. FENICHEL, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971) 193-226.
6. M. GORESKY and R. MACPHERSON, Stratified Morse Theory, Springer-Verlag, New York, 1980.
7. S. GONCHENKO, L. SHIL'NIKOV, and D. TUVAEV, On models with non-rough Poincaré homoclinic curves, Physica D 62 (1993), 1-14.
8. R. HARDT, Topological properties of subanalytic sets, Trans. A. M. S. 211 (1975) 57-70.
9. B. HASSELBLATT and A. KATOK, Introduction to the Modern Theory of Dynamical Systems, Encycl. of Math. and its Appl. 54, Cambridge University Press, Cambridge, 1995.
10. M. HIRSCH, C. PUGH, and M. SHUB, Invariant Manifolds, Lecture Notes in Math. 583, Springer-Verlag, New York, 1977.
11. B. HUNT, T. SAUER, and J. YORKE, Prevalence: a translation-invariant "almost every" on infinite dimensional spaces, Bull. A. M. S. (N.S.) 27 (1992), 217-238; Addendum: op. cit., 28 (1993), 306-307.
12. N. JACOBSON, Basic Algebra, Vol. I, W. H. Freeman and Co., San Francisco, 1974.
13. V. KALOSHIN, Generic diffeomorphisms with superexponential growth of number of periodic orbits, Stony Brook IMS preprint, ims99-2, http://www.math.sunysb.edu/ preprints.html, 1999.
14. _, Some prevalent properties of smooth dynamical systems, Tr. Mat. Inst. Steklova 213 (1997), 123-151.
15. D. MUMFORD, Algebraic Geometry. I. Complex Projective Varieties, Springer-Verlag, New York, 1976.
16. S. NEWHOUSE, Diffeomorphisms with infinitely many sinks, Topology 13 (1974), 9-18.
17. J. PALIS and W. DE MELO, Geometric Theory of Dynamical Systems, Springer-Verlag, New York, 1982.
18. E. PUJALS and M. SAMBARINO, Homoclinic tangencies and hyperbolicity for surface diffeomorphisms: A conjecture of Palis, Ann. of Math., to appear.
19. J. PALIS and F. TAKENS, Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations, Cambridge University Press, Cambridge, 1993.
20. C. ROBINSON, Bifurcation to infinitely many sinks, Comm. Math. Phys. 90 (1983), 433-459.
21. É. ROSALES GONSALES, On the growth in the number of periodic points of dynamical systems, Funct. Anal. Appl. 25 (1991), 254-262.
22. R. SACKER, A perturbation theorem for invariant manifolds and Hölder continuity, J. Math. Mech. 18 (1969), 705-762.
23. I. R. SHAFAREVICH, Basic algebraic geometry, 1. Varieties in Projective Space, Second edition, Springer-Verlag, New York, 1994.
24. S. SMALE, Differentiable dynamical systems, Bull. A.M.S. 73 (1967), 747-817.
25. 3) and the nongenericity of rational zeta functions, Trans. A.M.S. 174 (1972), 217-242.
26. L. TEDESCHINI-LALLI and J. A. YORKE, How often do simple dynamical processes have infinitely many coexisting sinks?, Comm. Math. Phys. 106 (1986), 635-657.
27. B. L. VAN DER WAERDEN, Modern Algebra, vol. I, Frederick Ungar Publishing Co. New York, 1949.