Topological invariance of the Collet-Eckmann condition for one-dimensional maps

This paper is devoted to studying the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several critical points the Collet-Eckmann condition is not in itself i...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2017-05, Vol.30 (5), p.2010-2022, Article 2010
Main Author: Li, Huaibin
Format: Article
Language:English
Subjects:
one-dimensional map
the Collet-Eckmann condition
the slow recurrence condition
topological invariance
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is devoted to studying the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several critical points the Collet-Eckmann condition is not in itself invariant under topological conjugacy. We show that the Collet-Eckmann condition together with any of several slow recurrence conditions is invariant under topological conjugacy. This extends and gives a new proof of a result by Luzzatto and Wang that also applies to the complex setting.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa67a1