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Rigidity in dynamics. (English) Zbl 1153.37370
Summary: We will review several results of rigidity in one-dimensional dynamics and its relation to renormalization. In many one dimensional dynamical systems the existence of a topological conjugacy between two mappings implies that the restriction of the conjugacy to the attractor extends to a smooth mapping. Thus the combinatorics imposes severe restrictions on the geometry of the attractor.
MSC:
37E05 Dynamical systems involving maps of the interval
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37E20 Universality and renormalization of dynamical systems
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Full Text: Euclid