Relative density of irrational rotation numbers in families of circle diffeomorphisms

Ergodic Theory and Dynamical Systems

Volumn 18, Issue 1, 1998, Pages 1-16

  Afraimovich, V ^a   Young, T ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032327501     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385798097648     Document Type: Article

References (22)

1. V. S. Afraimovich, S.-N. Chow and W.-S. Liu. Lorenz type attractors from a codimensional one bifurcation. Diff. Eqns. Dynam. Sys. 7 (1995), 375-407.
2. V. S. Afraimovich, W.-S. Liu and T. Young. Conventional multipliers for homoclinic orbits. Nonlinearity 9 (1996), 115-136.
3. V. S. Afraimovich and L. P. Shil'nikov. On some global bifurcations connected with disappearance of a saddle-node fixed point. Dokl. Akad. Nauk SSSR 219 (1974), 1281-1285. English transl. Soviet Math. Dokl. 15(3) (1974).
4. V. S. Afraimovich and L. P. Shil'nikov. On some global bifurcations connected with disappearance of a saddle-node fixed point. Dokl. Akad. Nauk SSSR 219 (1974), 1281-1285. English transl. Soviet Math. Dokl. 15(3) (1974).
5. V. I. Arnold. Small denominators I: Mappings of the circumference onto itself. Amer. Math. Soc. Trans. Ser. 2 46 (1965), 213-284.
6. J. Graczyk. Harmonic scaling for smooth families of diffeomorphisms of circle. Nonlinearity 4 (1991), 935-959.
7. J. Graczyk. Families of diffeomorphisms of the circle. Preprint.
8. M. Hermann. On differentiate conjugation of diffeomorphisms of the circle and of rotations. Publ. Math. Inst. Hautes Etud. Sci. 49 (1979), 5-233.
9. M. Hermann. Mesure de Lebesgue et nombre de rotation. Proc. Symp. Geometry and Topology (Lectures Notes in Mathematics, 597). Springer, New York, Berlin, 1971, pp. 271-293.
10. L. Jonker. Scaling of Arnold tongues for differential homeomorphisms of the circle. Comm. Math. Phys. 129 (1991), 1-25.
11. A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, 1995.
12. Y. Katznelson and D. Ornstein. The differentiability of the conjugation of certain diffeomorphisms of the circle. Ergod. Th. & Dynam. Sys. 9 (1989), 643-680.
13. K. Khanin and Ya. G. Sinai. A new proof of M. Hermann's theorem. Comm. Math. Phys. 112 (1987), 89-101.
14. K. Khanin and Ya. G. Sinai. Smoothness of conjugacies of diffeomorphisms of the circle with rotations. Russ. Math. Surv. 44 (1989), 69-99.
15. M. Kuozma, B. Choczewski, and R. Ger. Iterative Functional Equations. Cambridge University Press, 1990.
16. 1 Brunovsky hypothesis. J. Diff. Eqns. 113 (1994), 300-337.
17. W. de Melo and S. van Strien. One-dimensional Dynamics. Springer, New York, 1993.
18. S. Newhouse, J. Palis and F. Takens. Bifurcations and stability of families of diffeomorphisms. Bull. Amer. Math. Soc. 82 (1976), 499.
19. G. Świa̧tek. Rational rotation numbers from maps of the circle. Commun. Math. Phys. 119 (1988), 109-128.
20. M. Tsujii. Rotation number and one-parameter families of circle diffeomorphisms. Ergod. Th. & Dynam. Sys. 12 (1992), 359-363.
21. k conjugacy of 1-d diffeomorphisms with periodic points. Proc. Amer. Math. Soc. 125 (1997), 1987-1996.
22. J. Yoccoz. Conjugaison differentiable des diffeomorphismes du cercle dont le nombre de rotation verifie une condition diophantienne. Ann. Sci. Ecole Norm. Sup. 4 17 (1984), 333-359.