Transversality in the setting of hyperbolic and parabolic maps

Genadi Levin*, Weixiao Shen, Sebastian van Strien

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in [24] to treat unfolding of critical relations can also be used to deal with cases where the critical orbit converges to a hyperbolic attracting or a parabolic periodic orbit. As before this result applies to rather general families of maps, such as polynomial-like mappings, provided some lifting property holds. Our Main Theorem states that either the multiplier of a hyperbolic attracting periodic orbit depends univalently on the parameter and bifurcations at parabolic periodic points are generic, or one has persistency of periodic orbits with a fixed multiplier.

Original languageAmerican English
Pages (from-to)247-284
Number of pages38
JournalJournal d'Analyse Mathematique
Volume141
Issue number1
DOIs
StatePublished - Sep 2020

Bibliographical note

Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.

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