@article{PMIHES_2003__96__1_0, author = {Yampolsky, Michael}, title = {Hyperbolicity of renormalization of critical circle maps}, journal = {Publications Math\'ematiques de l'IH\'ES}, volume = {98}, year = {2003}, pages = {1-41}, mrnumber = {1985030}, zbl = {1030.37027}, language = {en}, url = {http://dml.mathdoc.fr/item/PMIHES_2003__96__1_0} }
Yampolsky, Michael. Hyperbolicity of renormalization of critical circle maps. Publications Mathématiques de l'IHÉS, Tome 98 (2003) pp. 1-41. http://gdmltest.u-ga.fr/item/PMIHES_2003__96__1_0/
[BR] Holomorphic families of injections, Acta Math., 157 (1986), 259-286. | MR 857675 | Zbl 0619.30027
and ,[Do] Does a Julia set depend continuously on the polynomial?, in Complex dynamical systems: The mathematics behind the Mandelbrot set and Julia sets, R. L. Devaney (ed.), Proc. of Symposia in Applied Math., Vol. 49, Amer. Math. Soc., 1994, pp. 91-138. | MR 1315535 | Zbl 0934.30023
,[DH1] Etude dynamique des polynômes complexes, I-II, Pub. Math. d'Orsay, 1984. | Zbl 0552.30018
and ,[DH2] On the dynamics of polynomial-like mappings, Ann. Sci. Éc. Norm. Sup., 18 (1985), 287-343. | Numdam | MR 816367 | Zbl 0587.30028
and ,[dF1] E. DE FARIA, Proof of universality for critical circle mappings, Thesis, CUNY, 1992.
[dF2] Asymptotic rigidity of scaling ratios for critical circle mappings, Ergodic Theory Dynam. Systems, 19 (1999), no. 4, 995-1035. | MR 1709428 | Zbl 0996.37045
,[dFdM1] Rigidity of critical circle mappings I, J. Eur. Math. Soc. (JEMS), 1 (1999), no. 4, 339-392. | MR 1728375 | Zbl 0988.37047
and ,[dFdM2] Rigidity of critical circle mappings II, J. Amer. Math. Soc., 13 (2000), no. 2, 343-370. | MR 1711394 | Zbl 0988.37048
and ,[Ep1] A. EPSTEIN, Towers of finite type complex analytic maps, PhD Thesis, CUNY, 1993.
[EKT] The set of maps with any given rotation interval is contractible, Commun. Math. Phys., 173 (1995), 313-333. | MR 1355627 | Zbl 0839.58021
, and ,[EY] A. EPSTEIN and M. YAMPOLSKY, The universal parabolic map. Erg. Th. & Dyn. Systems, to appear.
[EE] On the existence of fixed points of the composition operator for circle maps, Commun. Math. Phys., 107 (1986), 213-231. | MR 863640 | Zbl 0603.58004
and ,[FKS] M. FEIGENBAUM, L. KADANOFF, and S. SHENKER, Quasi-periodicity in dissipative systems. A renormalization group analysis, Physica, 5D (1982), 370-386. | MR 680571
[He] M. HERMAN, Conjugaison quasi-symmetrique des homeomorphismes analytiques du cercle a des rotations, manuscript.
[Keen] Dynamics of holomorphic self-maps of C, in Holomorphic functions and moduli I, D. DRASIN et al. (eds.), Springer-Verlag, New York, 1988. | MR 955806 | Zbl 0676.58011
,[Lan1] O. E. LANFORD, Renormalization group methods for critical circle mappings with general rotation number, in VIIIth International Congress on Mathematical Physics (Marseille, 1986), pp. 532-536, World Sci. Publishing, Singapore, 1987. | MR 915597
[Lan2] Renormalization group methods for critical circle mappings, Nonlinear evolution and chaotic phenomena, NATO Adv. Sci. Inst. Ser. B: Phys., 176, pp. 25-36, Plenum, New York, 1988. | Zbl 0707.58043
,[Lyu2] Renormalization ideas in conformal dynamics, Cambridge Seminar “Current Developments in Math.”, May 1995, pp. 155-184, International Press, 1995, Cambridge, MA. | Zbl 0877.58046
,[Lyu3] Dynamics of quadratic polynomials, I-II, Acta Math., 178 (1997), 185-297. | MR 1459261 | Zbl 0908.58053
,[Lyu4] Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture, Ann. of Math. (2), 149 (1999), no. 2, 319-420. | Zbl 0945.37012
,[Lyu5] Almost every real quadratic map is either regular or stochastic, Ann. of Math. (2), 156 (2002), no. 1, 1-78. | MR 1935840 | Zbl pre01850538
,[LY] Dynamics of quadratic polynomials: complex bounds for real maps, Ann. l'Inst. Fourier 47, 4 (1997), 1219-1255. | Numdam | Zbl 0881.58053
and ,[MP] Universal small-scale structure near the boundary of Siegel disks of arbitrary rotation number, Physica, 26D (1987), 193-202. | MR 892444 | Zbl 0612.58028
and ,[MSS] On the dynamics of rational maps, Ann. Sci. Éc. Norm. Sup., 16 (1983), 193-217. | Numdam | MR 732343 | Zbl 0524.58025
, and ,[McM1] Complex dynamics and renormalization, Annals of Math. Studies, v.135, Princeton Univ. Press, 1994. | MR 1312365 | Zbl 0822.30002
,[McM2] Renormalization and 3-manifolds which fiber over the circle, Annals of Math. Studies, Princeton University Press, 1996. | MR 1401347 | Zbl 0860.58002
,[Mes] B. D. MESTEL, A computer assisted proof of universality for cubic critical maps of the circle with golden mean rotation number, PhD Thesis, University of Warwick, 1985.
[Mil] Dynamics in one complex variable, Introductory lectures, Friedr. Vieweg & Sohn, Braunschweig, 1999. | MR 1721240 | Zbl 0946.30013
,[MvS] One dimensional dynamics, Springer, 1993. | MR 1239171 | Zbl 0791.58003
and ,[ORSS] Universal properties of the transition from quasi- periodicity to chaos in dissipative systems, Physica, 8D (1983), 303-342. | MR 719630 | Zbl 0538.58025
, , , and ,[Sul1] Quasiconformal homeomorphisms and dynamics, topology and geometry, Proc. ICM-86, Berkeley, v. II, 1216-1228. | MR 934326 | Zbl 0698.58030
,[Sul2] Bounds, quadratic differentials, and renormalization conjectures, AMS Centennial Publications, 2, Mathematics into Twenty-first Century (1992). | MR 1184622 | Zbl 0936.37016
,[Sh] The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets, Ann. of Math. (2), 147 (1998), no. 2, 225-267. | MR 1626737 | Zbl 0922.58047
,[Sw1] Rational rotation numbers for maps of the circle, Commun. Math. Phys., 119 (1988), 109-128. | MR 968483 | Zbl 0656.58017
,[Ya1] Complex bounds for renormalization of critical circle maps, Erg. Th. & Dyn. Systems, 19 (1999), 227-257. | MR 1677153 | Zbl 0918.58049
,[Ya2] The attractor of renormalization and rigidity of towers of critical circle maps, Commun. Math. Phys., 218 (2001), no. 3, 537-568. | MR 1828852 | Zbl 0978.37033
,[Ya3] M. YAMPOLSKY, The global horseshoe for the renormalization of critical circle maps, Preprint, 2002.
[Yoc] Il n'ya pas de contre-example de Denjoy analytique, C.R. Acad. Sci. Paris, 298 (1984) série I, 141-144. | Zbl 0573.58023
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