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Bifurcation frequency for unimodal maps

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Abstract

We consider some natural one-parameter unfoldingsf μ, of a unimodal mapf 0 whose periodic points are hyperbolic and whose critical point is nondegenerate and eventually periodic. Among other facts, it follows from our theorems that, if the Julia set off 0 does not contain intervals, the relative measure of the bifurcation set is zero at zero.

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Communicated by Ya. G. Sinai

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Vargas, E. Bifurcation frequency for unimodal maps. Commun.Math. Phys. 141, 633–650 (1991). https://doi.org/10.1007/BF02102821

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  • DOI: https://doi.org/10.1007/BF02102821

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