Generic diffeomorphisms with superexponential growth of number of periodic orbits

Communications in Mathematical Physics

Volumn 211, Issue 1, 2000, Pages 253-271

  Kaloshin, Vadim Yu ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349439     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050811     Document Type: Article

References (26)

1. [AM] Artin, M., Mazur, B.: Periodic orbits. Annals of Math. 81, 82-99 (1965)
2. [Ba] Baladi, V.; Dynamical zeta functions, Series C: Mathematical and Physical Sciences, vol. 464 in Real and Complex dynamical systems, edited by B. Branner & P. Hjorth
3. [BC] Benedicks, M., Carleson, L.: Dynamics of the Henon map. Annals of Math. 133 73-169 (1991)
4. [BD] Bonatti, C., Diaz, Z.: Connexions hétéroclines ae généricité d'une infinité ou se sources. Prepublications du Laboraroire de Topologie, Dijon
5. [Bo] Bowen, R.: On Axiom A diffeomorphisms. Regional Conference Series in Mathematics, no. 35, Providence, R1: AMS, 1978
6. [Fe] Fenichel, N.: Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193-226 (1971)
7. [GST] Gonchenko, S.V., Shil'nikov, L.P. and Tuvaev, D.V.: On models with non-rough Poincaré homoclinic curves. Physica D 62, 1-14 (1993)
8. [GST2] Gonchenko, S.V., Shil'nikov, L.P. and Tuvaev, D.V.: Homoclinic tangendes of an arbitrary order in Newhouse's domains (in Russian). Preprint
9. [HK] Hasselblatt, B., Katok, A.: Introduction to the modern theory of dynamical systems. Encyclopedia of Mathematics and its Applications. 54. Cambridge: Cambridge University Press, 1995
10. [HPS] Hirsch, M., Pugh, C., Shub, M.: Invariant manifolds. Lecture Notes in Mathematics, Vol. 583. Berlin-New York: Springer-Verlag, 1977
11. [IY] Ilyashenko, Yu.S., Yakovenko, S. Yu.: Finitely-Smooth normal forms for local families of diffeomorphisms and vector fields. Russ. Math. Survey (46), no. 1, 1-43 (1991)
12. [K1] Kaloshin, V.Yu.: An extension of Artin-Mazur theorem. Annals of Math. 150, no. 2, 729-741
13. [K2] Kaloshin, V.Yu.: Generic diffeomorphisms with superexponential growth of the number of periodic points. Stony Brook IMS perprint server, #99/2, web address http://www.math.sunysb.edu/preprints.html
14. [MV] Mora, L., Viana, M.: Abundance of strange attractors. Acta Math. 171, 1-71 (1993)
15. [N] Newhouse, S.: Diffeomorphisms with infinitely many sinks. Topology 13, 9-18 (1974)
16. [O] Oxtoby, J.: Measure and category. A survey of the analogies between topological and measure spaces. Second edition. Graduate Texts in Mathematics, 2, New York-Berlin: Springer-Verlag, 1980
17. [PM] Palis, J., de Melo, V.: Geometric Theory of Dynamical Systems. Berlin-Heidelberg-New York: Springer-Verlag, 1982
18. [PT] Palis, J. & Takens, F.: Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations. Cambridge: Cambridge University Press, 1993
19. [PS] Pujals, E., Sambarino, M.: omoclinic tangencies and hyperbolicity for surface diffeomorphisms: A conjecture of Palis. To appear in Annals of Math.
20. [Rb] Robinson, C.: Bifurcation to infinitely many sinks. Commun. Math. Phys. 106, 433-459 (1983)
21. [Rm] Romero, N.: Persistence of homoclinic tangencies in higher dimensions. Ergodic Theory Dynam. Systems 15, no. 4, 735-757 (1995)
22. [RG] Rozales-Gorsalez, E.: Growth of periodic orbits of dynamical systems. Funcz. Anal. Appl. 25, (4), 254-262 (1991)
23. [Sa] Sacker, R.: A perturbation theorem for invariant manifolds and Holder continuity. J. Math. Mech. 18, 705-762 (1969)
24. 3) and the nondegenericity of rational zeta functions. Trans. of Amer. Math. Soc. Vol.174, 217-242 (1973)
25. [Sm] Smale, S.: Differentiable Dynamical Systems. Bull. Amer. Math. Soc. 73, 747-817 (1967)
26. [TY] Tedeschini-Lalli, L. & Yorke, J.A.: Infinitely many coexisting sinks. Commun. Math. Phys. 106, 635-657 (1986)