Transversality in the setting of hyperbolic and parabolic maps
File(s)
Working paper
Author(s)
Levin, Genadi
Shen, Weixiao
Strien, Sebastian van
Type
Working Paper
Abstract
In this paper we consider families of holomorphic maps defined on subsets of
the complex plane, and show that the technique developed in \cite{LSvS1} 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.
the complex plane, and show that the technique developed in \cite{LSvS1} 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
2019-01-28
Citation
2019
Publisher
arXiv
Copyright Statement
© 2019 The Author(s)
Sponsor
Commission of the European Communities
Identifier
http://arxiv.org/abs/1901.09941v1
Grant Number
339523
Subjects
math.DS
math.DS
37-xx, 30-xx
Publication Status
Published