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

van Strien, Sebastian

Fundamenta Mathematicae, Tome 163 (2000), p. 39-54 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $λ \mapsto (f_{λ}^{k_{1}} (c_{1} (λ)) - p_{1} (λ), . . ., f_{λ}^{k_{d - 2}} (c_{d - 2} (λ)) - p_{d - 2} (λ))$ is a local diffeomorphism for λ near $λ_{0}$ . For quadratic families this result was proved previously in DH using entirely different methods.

Publié le : 2000-01-01

Zbl 0965.37038

EUDML-ID : urn:eudml:doc:212428

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     author = {Sebastian van Strien},
     title = {Misiurewicz maps unfold generically (even if they are critically non-finite)},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {39-54},
     zbl = {0965.37038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p39bwm}
}

van Strien, Sebastian. Misiurewicz maps unfold generically (even if they are critically non-finite). Fundamenta Mathematicae, Tome 163 (2000) pp. 39-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p39bwm/

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