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TY - CHAP
TI - Conclusion
A2 - McMullen, Curtis T.
AB - In this chapter we briefly recapitulate the analogies between the action of a mapping class*ψ*:*AH*(*S*) →*AH*(*S*) and the action of a renormalization operator${{\mathcal{R}}_{p}}:{{\mathcal{H}}^{(p)}}\to \mathcal{H}$. We also discuss some open problems on both sides of the dictionary. These parallels and problems were summarized in Tables 1.1 and 1.2 of §1.

Consider first the algorithms for the construction of fixed points, detailed in §3.4 for*ψ*and in §7.1 for${{\mathcal{R}}_{p}}$. In each case, the dynamics at the fixed point seems to be hyperbolic, with both expanding and contracting directions. The fixed point cannot be located

EP - 182
PB - Princeton University Press
PY - 1996
SN - 9780691011530
SP - 175
T2 - Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142)
UR - http://www.jstor.org/stable/j.ctt7ztfmd.12
Y2 - 2021/09/26/
ER -