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

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UNSPECIFIED.
(2000)
*Misiurewicz maps unfold generically (even if they are critically non-finite).*
FUNDAMENTA MATHEMATICAE, 163
(1).
pp. 39-54.
ISSN 0016-2736

**Full text not available from this repository.**

## Abstract

We show that in normalized families of polynomial or rational maps, Misiurewicz maps (critically finite or infinite) unfold generically. For example, if f(lambda 0) is critically finite with non-degenerate critical point c(1)(lambda(0)),...,c(n)(lambda(0)) such that f(lambda 0)(ki) (c(i)(lambda(0))) = p(i)(lambda(0)) are hyperbolic periodic points for i = 1,..., n, then

lambda --> (f(lambda)(k1)(c(1)(lambda)) - p(1)(lambda),...,f(lambda)(kd-2) (c(d-2)(lambda)) - p(d-2)(lambda))

is a local diffeomorphism for lambda near lambda(0). For quadratic families this result was proved previously in [DH] using entirely different methods.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | FUNDAMENTA MATHEMATICAE |

Publisher: | POLISH ACAD SCIENCES INST MATHEMATICS |

ISSN: | 0016-2736 |

Official Date: | 2000 |

Volume: | 163 |

Number: | 1 |

Number of Pages: | 16 |

Page Range: | pp. 39-54 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/13043 |

Data sourced from Thomson Reuters' Web of Knowledge

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