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Misiurewicz maps unfold generically (even if they are critically non-finite)

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van Strien S.

Fundamenta Mathematicae

2000

tom 163

nr 1

39-54

We show that in normalized families of polynomial or rational maps, Misiurewicz maps (critically finite or infinite) unfold generically. For example, if $f_{λ_0}$ is critically finite with non-degenerate critical point $c_1(λ_0),...,c_n(λ_0)$ such that $f_{λ_0}^{k_i}(c_i(λ_0)) = p_i(λ_0)$ are hyperbolic periodic points for i = 1,...,n, then IV-1. Age impartible......................................................................................................................................................................... 31 $λ ↦ (f_λ^{k_1}(c_1(λ))-p_1(λ),..., f_λ^{k_{d-2}}(c_{d-2}(λ))-p_{d-2}(λ))$ is a local diffeomorphism for λ near $λ_0$. For quadratic families this result was proved previously in {DH} using entirely different methods.

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1 Fundamenta Mathematicae

1 van Strien S.

1 2000

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Misiurewicz maps unfold generically (even if they are critically non-finite)