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Ziggurats and rotation numbers
1. | DPMMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom |
2. | Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, United States |
References:
[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.
doi: 10.1090/S0002-9947-05-03754-2. |
[3] |
D. Calegari, Stable commutator length is rational in free groups, Jour. Amer. Math. Soc., 22 (2009), 941-961.
doi: 10.1090/S0894-0347-09-00634-1. |
[4] |
D. Calegari, Faces of the scl norm ball, Geom. Topol., 13 (2009), 1313-1336.
doi: 10.2140/gt.2009.13.1313. |
[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.
doi: 10.1017/S0143385709000662. |
[7] |
D. Calegari and J. Louwsma, Immersed surfaces in the modular orbifold, Proc. Amer. Math. Soc., 139 (2011), 2295-2308.
doi: 10.1090/S0002-9939-2011-10911-0. |
[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.
doi: 10.1007/BF02566232. |
[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.
doi: 10.1090/conm/058.3/893858. |
[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.
doi: 10.1007/BF01456075. |
[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.
doi: 10.1007/BF01388709. |
[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.
doi: 10.1007/BF02564479. |
[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.
doi: 10.1007/BF01218263. |
[20] |
W. Thurston, Three-manifolds, foliations and circles, I,, preprint, ().
|
[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. |
show all references
References:
[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.
doi: 10.1090/S0002-9947-05-03754-2. |
[3] |
D. Calegari, Stable commutator length is rational in free groups, Jour. Amer. Math. Soc., 22 (2009), 941-961.
doi: 10.1090/S0894-0347-09-00634-1. |
[4] |
D. Calegari, Faces of the scl norm ball, Geom. Topol., 13 (2009), 1313-1336.
doi: 10.2140/gt.2009.13.1313. |
[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.
doi: 10.1017/S0143385709000662. |
[7] |
D. Calegari and J. Louwsma, Immersed surfaces in the modular orbifold, Proc. Amer. Math. Soc., 139 (2011), 2295-2308.
doi: 10.1090/S0002-9939-2011-10911-0. |
[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.
doi: 10.1007/BF02566232. |
[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.
doi: 10.1090/conm/058.3/893858. |
[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.
doi: 10.1007/BF01456075. |
[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.
doi: 10.1007/BF01388709. |
[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.
doi: 10.1007/BF02564479. |
[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.
doi: 10.1007/BF01218263. |
[20] |
W. Thurston, Three-manifolds, foliations and circles, I,, preprint, ().
|
[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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