Journal of Modern Dynamics (JMD)

Ziggurats and rotation numbers
Pages: 711 - 746, Issue 4, October 2011

doi:10.3934/jmd.2011.5.711      Abstract        References        Full text (1092.6K)           Related Articles

Danny Calegari - DPMMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom (email)
Alden Walker - Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, United States (email)

1 R. Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. No., 50 (1979), 11-25.       
2 D. Calegari, Dynamical forcing of circular groups, Trans. Amer. Math. Soc., 358 (2006), 3473-3491.       
3 D. Calegari, Stable commutator length is rational in free groups, Jour. Amer. Math. Soc., 22 (2009), 941-961.       
4 D. Calegari, Faces of the scl norm ball, Geom. Topol., 13 (2009), 1313-1336.       
5 D. Calegari, "scl," MSJ Memoirs, 20, Mathematical Society of Japan, Tokyo, 2009.       
6 D. Calegari and K. Fujiwara, Combable functions, quasimorphisms, and the central limit theorem, Erg. Theory Dyn. Sys., 30 (2010), 1343-1369.       
7 D. Calegari and J. Louwsma, Immersed surfaces in the modular orbifold, Proc. Amer. Math. Soc., 139 (2011), 2295-2308.       
8 D. Eisenbud, U. Hirsch and W. Neumann, Transverse foliations of Seifert bundles and self-homeomorphism of the circle, Comment. Math. Helv., 56 (1981), 638-660.       
9 É. Ghys, Groupes d'homéomorphismes du cercle et cohomologie bornée, in "The Lefschetz Centennial Conference, Part III" (Mexico City, 1984), Contemp. Math., 58, III, Amer. Math. Soc., Providence, RI, (1987), 81-106.       
10 É. Ghys, Groups acting on the circle, Enseign. Math. (2), 47 (2001), 329-407.       
11 M. Herman, Sur la conjugaison différentiable des diffeomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. No., 49 (1979), 5-233.       
12 M. Jankins and W. Neumann, Rotation numbers of products of circle homeomorphisms, Math. Ann., 271 (1985), 381-400.       
13 A. Katok and B. Hasselblatt, "An Introduction to the Modern Theory of Dynamical Systems," Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995.       
14 S. Katok, "Fuchsian Groups," Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992.       
15 S. Matsumoto, Some remarks on foliated $S^1$ bundles, Invent. Math., 90 (1987), 343-358.       
16 W. de Melo and S. van Strien, "One-Dimensional Dynamics," Ergeb. der Math. und ihrer Grenz. (3), 25, Springer-Verlag, Berlin, 1993.       
17 R. Naimi, Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv., 69 (1994), 155-162.       
18 F. Przytycki and M. Urbański, Conformal fractals: Ergodic theory methods, LMS Lect. Note Ser., 371, Cambridge University Press, Cambridge, 2010.       
19 G. Światek, Rational rotation numbers for maps of the circle, Comm. Math. Phys., 119 (1988), 109-128.       
20 W. Thurston, Three-manifolds, foliations and circles, I, preprint, arXiv:math/9712268.
21 M. Urbański, Parabolic Cantor sets, Fund. Math., 151 (1996), 241-277.       
22 J.-C. Yoccoz, Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne, Ann. Sci. École Norm. Sup. (4), 17 (1984), 333-359.       

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