Dimension of the boundary of quasiconformal Siegel disks

Inventiones Mathematicae

Volumn 148, Issue 3, 2002, Pages 465-493

  Graczyk, Jacek ^a   Jones, Peter ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b Department of Mathematics ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036016730     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220100198     Document Type: Article

References (29)

1. Ahlfors, L.V.: Lectures on Quasiconformal Mappings, Wadsworth, Brooks/Cole, Monterey, CA, 1987
2. Ahlfors, L.V.: Conformal invariants, McGraw-Hill Book Company, USA, 1973
3. 2 estimates and the Schwarzian derivative, J. Anal. Math. 62 (1994), 77-113
4. Bishop, C., Jones, P.: Wiggly sets and limit sets, Ark. Mat. 35 (1997), 201-224
5. Buff, X., Henriksen, C.: Scaling ratios and triangles in Siegel disks, Math. Res. Lett. 6 (1999), no. 3-4, 293-305
6. Burbanks, A.D., Osbaldestin, A.H., Stirnemann, A: Fractal dimension of Siegel disc boundaries, manuscript 1998
7. Douady, A.: Disques de Siegel et annaux de Herman, Astérisque 152-153 (1987-88), 151-172
8. Fernández, J.L., Heinonen, J., Martio, O.: Quasilines and Conformal Mappings, J. Anal. Math. 52 (1989), 117-132
9. Gerhing, F.:Characteristic Properties of Quasidisks, Presses de l'Université de Montreal, Montreal, Que. (1982), 99pp
10. Ghys, E.: Transformations holomorphes au voisinage d'une courbe de Jordan, C.R. Acad. Sci. Paris Sér I Math. 298 (1984), 385-388
11. Graczyk, J., Świa̧tek, G.: Critical circle maps near bifurcation, Commun. Math. Phys. 176 (1996), 227-260
12. Graczyk, J., Świa̧tek, G.:Singular Measures in Cirle Dynamics, Commun. Math. Phys. 157 (1993), 213-230
13. Jones, P.: private communication
14. Herman, M.: Conjugaison quasi symmetric des homéomorphismes analytiques du cercle à des rotations, manuscript (1987)
15. Herman, M.: Are there critical points on the boundaries of singular domains?, Comm. Math. Phys. 99 (1985), 593-612
16. Herman, M.: Conjugaison quasisymétric des difféomorphismes du cercle à des rotations et applications aux disques singulier de Siegel, manuscript
17. Manton, N.S., Nauenberg, M.: Universal scaling behaviour for iterated maps in the complex plane, Comm. Math. Phys. 89 (1983), 555-570
18. McMullen, C.: Self-similarity of Siegel disks and Hausdorff dimension of Julia sets, Acta Math. 180 (1998), 247-292
19. Perez-Marco, R.: Fixed points and circle maps, Acta Math. 179 (1997), 243-294
20. Perez-Marco, R.: Siegel disks with smooth boundary, preprint 1997
21. Petersen, C.: private communication
22. Pomerenke, C.: Boundary Behaviour of Conformal Maps, Springer-Verlag, New York (1992)
23. Rhode, S.: On Conformal Welding and Quasicircles, Michigan Math. J. 38 (1991), 111-116
24. Siegel, C.L.: Iterations of analytic functions, Ann. Math. 43 (1942), 807-812
25. Świa̧tek, G.: Rational rotation number for maps of the circle, Commun. Math. Phys. 119 (1988), 109-128
26. Świa̧tek, G.: On critical circle homeomorphisms, Bol. Soc. Bras. Mat. 29 (1998) 329-351
27. Widom, M.: Renormalization group analysis of quasi-periodicity in analytic maps. Comm. Math. Phys. 92 (1983), 121-136
28. Yoccoz, J-C.: Cojugaisons des difféomorphismes analytiques du cercle, manuscript
29. Yoccoz, J.-C.: Il n'y a pas de contre-exemple de Denjoy analitique, C.R. Acad. Sci. Paris, Série I 298 (1984), 141-144