Transversality in the setting of hyperbolic and parabolic maps
File(s)
Accepted version
Author(s)
Levin, Genadi
Shen, Weixiao
van Strien, Sebastian
Type
Journal Article
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.
Date Issued
2020-09-01
Date Acceptance
2020-05-15
Citation
Journal d'Analyse Mathematique, 2020, 141 (1), pp.247-284
ISSN
0021-7670
Publisher
Springer Nature [academic journals on nature.com]
Start Page
247
End Page
284
Journal / Book Title
Journal d'Analyse Mathematique
Volume
141
Issue
1
Copyright Statement
© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11854-020-0130-7
Sponsor
Commission of the European Communities
Grant Number
339523
Subjects
Science & Technology
Physical Sciences
Mathematics
HOLOMORPHIC MOTIONS
RUELLE-OPERATOR
MONOTONICITY
DYNAMICS
FAMILIES
ENTROPY
PROOF
General Mathematics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2020-11-12