@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},
pages = {1--41},
year = {2003},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {96},
mrnumber = {1985030},
zbl = {1030.37027},
language = {en},
url = {https://www.numdam.org/item/PMIHES_2003__96__1_0/}
}
TY - JOUR AU - Yampolsky, Michael TI - Hyperbolicity of renormalization of critical circle maps JO - Publications Mathématiques de l'IHÉS PY - 2003 SP - 1 EP - 41 VL - 96 PB - Institut des Hautes Etudes Scientifiques UR - https://www.numdam.org/item/PMIHES_2003__96__1_0/ LA - en ID - PMIHES_2003__96__1_0 ER -
Yampolsky, Michael. Hyperbolicity of renormalization of critical circle maps. Publications Mathématiques de l'IHÉS, Tome 96 (2003), pp. 1-41. https://www.numdam.org/item/PMIHES_2003__96__1_0/
[BR] and , Holomorphic families of injections, Acta Math., 157 (1986), 259-286. | Zbl | MR
[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. | Zbl | MR
[DH1] and , Etude dynamique des polynômes complexes, I-II, Pub. Math. d'Orsay, 1984. | Zbl
[DH2] and , On the dynamics of polynomial-like mappings, Ann. Sci. Éc. Norm. Sup., 18 (1985), 287-343. | Numdam | Zbl | MR | EuDML
[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. | Zbl | MR
[dFdM1] and , Rigidity of critical circle mappings I, J. Eur. Math. Soc. (JEMS), 1 (1999), no. 4, 339-392. | Zbl | MR | EuDML
[dFdM2] and , Rigidity of critical circle mappings II, J. Amer. Math. Soc., 13 (2000), no. 2, 343-370. | Zbl | MR
[Ep1] A. EPSTEIN, Towers of finite type complex analytic maps, PhD Thesis, CUNY, 1993.
[EKT] , and , The set of maps with any given rotation interval is contractible, Commun. Math. Phys., 173 (1995), 313-333. | Zbl | MR
[EY] A. EPSTEIN and M. YAMPOLSKY, The universal parabolic map. Erg. Th. & Dyn. Systems, to appear.
[EE] and , On the existence of fixed points of the composition operator for circle maps, Commun. Math. Phys., 107 (1986), 213-231. | Zbl | MR
[FKS] M. FEIGENBAUM, L. KADANOFF, and S. SHENKER, Quasi-periodicity in dissipative systems. A renormalization group analysis, Physica, 5D (1982), 370-386. | MR
[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. | Zbl | MR
[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
[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
[Lyu2] , Renormalization ideas in conformal dynamics, Cambridge Seminar “Current Developments in Math.”, May 1995, pp. 155-184, International Press, 1995, Cambridge, MA. | Zbl
[Lyu3] , Dynamics of quadratic polynomials, I-II, Acta Math., 178 (1997), 185-297. | Zbl | MR
[Lyu4] , Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture, Ann. of Math. (2), 149 (1999), no. 2, 319-420. | Zbl
[Lyu5] , Almost every real quadratic map is either regular or stochastic, Ann. of Math. (2), 156 (2002), no. 1, 1-78. | MR
[LY] and , Dynamics of quadratic polynomials: complex bounds for real maps, Ann. l'Inst. Fourier 47, 4 (1997), 1219-1255. | Zbl | Numdam
[MP] and , Universal small-scale structure near the boundary of Siegel disks of arbitrary rotation number, Physica, 26D (1987), 193-202. | Zbl | MR
[MSS] , and , On the dynamics of rational maps, Ann. Sci. Éc. Norm. Sup., 16 (1983), 193-217. | Zbl | MR | Numdam
[McM1] , Complex dynamics and renormalization, Annals of Math. Studies, v.135, Princeton Univ. Press, 1994. | Zbl | MR
[McM2] , Renormalization and 3-manifolds which fiber over the circle, Annals of Math. Studies, Princeton University Press, 1996. | Zbl | MR
[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. | Zbl | MR
[MvS] and , One dimensional dynamics, Springer, 1993. | Zbl | MR
[ORSS] , , , and , Universal properties of the transition from quasi- periodicity to chaos in dissipative systems, Physica, 8D (1983), 303-342. | Zbl | MR
[Sul1] , Quasiconformal homeomorphisms and dynamics, topology and geometry, Proc. ICM-86, Berkeley, v. II, 1216-1228. | Zbl | MR
[Sul2] , Bounds, quadratic differentials, and renormalization conjectures, AMS Centennial Publications, 2, Mathematics into Twenty-first Century (1992). | Zbl | MR
[Sh] , The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets, Ann. of Math. (2), 147 (1998), no. 2, 225-267. | Zbl | MR
[Sw1] , Rational rotation numbers for maps of the circle, Commun. Math. Phys., 119 (1988), 109-128. | Zbl | MR
[Ya1] , Complex bounds for renormalization of critical circle maps, Erg. Th. & Dyn. Systems, 19 (1999), 227-257. | Zbl | MR
[Ya2] , The attractor of renormalization and rigidity of towers of critical circle maps, Commun. Math. Phys., 218 (2001), no. 3, 537-568. | Zbl | MR
[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






