M. Lyubich, Renormalization Ideas in Conformal Dynamics, Cambridge Seminar \Current Developments in Math.", May 1995. International Press, 1995. Cambridge, MA, 155-184. Home/Search Document Details and Download
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Fibonacci Fixed Point of Renormalization - Buff (2000) (Correct)
....degree 4 have since been studied by van Strien and Nowicki in [SN] where they obtained new results using renormalization techniques. We would like to use results by H. Epstein [E1] E2] on xed points of renormalization to improve the results obtained by van Strien and Nowicki. In his survey [Ly4], Lyubich describes renormalization in the following way: the notion of renormalization of a dynamical system f consists in taking a small piece of the dynamical space, considering the rst return map to this piece, and then rescale it to the original size. The new dynamical system is called ....
....(1997) Fixed points of renormalization. 2 studied (see Collet and Eckmann and Lanford [CE] CEL] and [La] Cvitanovi c [Cv] Eckmann and Wittwer [EW] Vul, Sinai and Khanin [VSK] Epstein [E1] and [E2] Sullivan [S] de Melo and van Strien [dMvS] McMullen [McM1] and [McM2] Lyubich [Ly3] [Ly4], Ly5] and [Ly6] For a historical account, the reader is invited to consult [T] or [Ly5] Lyubich generalized the notion of renormalization for polynomial like mappings, to a wider class of maps, that we will call L maps. This allowed him to apply the renormalization ideas to ....
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M. Lyubich, Renormalization Ideas in Conformal Dynamics, Cambridge Seminar \Current Developments in Math.", May 1995. International Press, 1995. Cambridge, MA, 155-184.
Pasting Together Julia Sets - a worked out example of mating - Milnor (1997) (Correct)
....f 1 and f 2 . The uniqueness question for matings is part of a larger rigidity question: If two quadratic rational maps are topologically conjugate under an orientation preserving homeomorphism which is holomorphic on the Fatou set, does it follow that they are holomorphically conjugate (Compare Lyubich [1995, x5] The only known counterexamples to the corresponding statement in higher degrees are Latt es mappings of degree d = n 2 4 . Compare Appendix B.5(a) Here is a trivial example. Suppose that f 2 (z) z 2 , so that K 2 is the closed unit disk. Pasting the boundaries of K 1 and K 2 ....
M. Lyubich, Renormalization ideas in conformal dynamics, pp. 109-133 of \Current Developments in Mathematics, 1995", edit. Bott, Ja e, Yau, International Press 1995.
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