On the scaling structure for period doubling
Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), 20 p. 
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     author = {Birkhoff, Garrett and Martens, Marco and Tresser, Charles},
     title = {On the scaling structure for period doubling},
     booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
     editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {286},
     year = {2003},
     zbl = {1156.37310},
     mrnumber = {2052301},
     language = {en},
     url = {http://www.numdam.org/item/AST_2003__286__167_0/}
}
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Birkhoff, Garrett; Martens, Marco; Tresser, Charles. On the scaling structure for period doubling, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), 20 p. http://www.numdam.org/item/AST_2003__286__167_0/

[AMM] A. Avila, M. Martens, W. De Melo, On the dynamics of the renormalization operator, Global Analysis of Dynamical Systems, (Festschrift dedicated to Floris Takens for his 60th birthday), W. Broer, B. Krauskopf, and G. Vegter Eds. IOP Publishing Ltd 2001, 449-461. | MR 1858468 | Zbl 1198.37068

[CT] P. Coullet, C. Tresser, Itérations d'endomorphismes et groupe de renormalisation, J. Phy. C5 (1978), 25-28. | MR 512110 | Zbl 0402.54046

[E1] H. Epstein, New proofs of the existence of the Feigenbaum functions, Commun. Math.Phys. 106 395-426 (1986). | Article | MR 859818 | Zbl 0608.30031

[E2] H. Epstein, Fixed points of composition operators II, Nonlinearity 2 305-310 (1989). | Article | MR 994095 | Zbl 0731.39007

[EL] H. Epstein, O. E. Lanford, personal communications.

[F] M. J. Feigenbaum, The transition to aperiodic behavior in turbulent systems, Commun. Math. Phys. 77 (1980), 65-86. | Article | MR 588687 | Zbl 0465.76050

[GT] J. M. Gambaudo, C. Tresser, Self-similar constructions in smooth dynamics: Rigidity, Smoothness, and Dimension, Commun. Math. Phys. 150 (1992), 45-58. | Article | MR 1188495 | Zbl 0771.58035

[KSV] K. M. Khanin, Ya. Sinai, E. B. Vul, Feigenbaum universality and thermodynamic formalism, Uspekhi Mat. Nauk 39 (1984) 3-37. | MR 747790 | Zbl 0561.58033

[La] O. E. Lanford Iii, A computer assisted proof of the Feigenbaum conjecture, Bull. Amer. Math. Soc. (N.S.) 6 (1984), 427-434. | Article | MR 648529 | Zbl 0487.58017

[Ly] M. Lyubich, Feigenbaum-Coullet-Tresser Universality and Milnor's Hairriness Conjecture, Ann. of Math. 149 (1999), 319-420. | Article | EuDML 120519 | MR 1689333 | Zbl 0945.37012

[Ma1] M. Martens, Distortion Results and Invariant Cantor Sets of Unimodal Maps, Erg. Th. & Dyn. Sys. 14 (1994), 331-349. | Article | MR 1279474 | Zbl 0809.58026

[Ma2] M. Martens, The Periodic Points of Renormalization, Ann. of Math. 147 (1998), 543-584. | Article | MR 1637651 | Zbl 0936.37017

[dMvS] W. De Melo, S. Van Strien, One-dimensional Dynamics, (Springer-Verlag, Berlin, 1993). | MR 1239171 | Zbl 0791.58003

[Mc] C. Mcmullen, Complex Dynamics and Renormalization, Ann. of Math., Studies 135, (Princeton University Press, Princeton, 1994). | MR 1312365 | Zbl 0822.30002

[R] D. A. Rand, Global phase space universality, smooth conjugacy and renormalization: I. The C 1+∞ case, Nonlinearity 1 (1988), 181-202. | Article | MR 928952 | Zbl 0697.58029

[S1] D. Sullivan, Differentiable structure on fractal like sets, determined by intrinsic scaling functions on dual Cantor sets, The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. in Pure Math. 48, 15-23. (Amer. Math. Soc, Providence, RI, 1988). | Article | MR 974329 | Zbl 0665.58027

[S2] D. Sullivan, Bounds, Quadratic Differentials, and Renormalization Conjectures, in A.M.S. Centennial Publication Vol 2 Mathematics into the Twenty-first Century (Am. Math. Soc., Providence, RI, 1992). | MR 1184622 | Zbl 0936.37016

[T] C. Tresser, Fine structure of universal Cantor sets, in Instabilities and Nonequilibrium Structures III, E. Tirapegui and W. Zeller Eds., (Kluwer, Dordrecht-Boston-London, 1991). | MR 1177835