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

• Autorzy: Sebastian van Strien
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37G99: None of the above, but in this section
• 32H50: Iteration problems
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 1
• Strony: 39-54

Daty

wydano

2000

otrzymano

1999-04-21

poprawiono

1999-09-23

Twórcy

autor

Sebastian van Strien

• Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom

Bibliografia

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