Gluing orbit property and partial hyperbolicity

This article is a follow up of our recent works [7,8], and here we discuss the relation between the gluing orbit property and partial hyperbolicity. First we prove that a partially hyperbolic diffeomorphism with two saddles with different index, and such that the stable manifold of one of these sadd...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2021-01, Vol.272, p.203-221
Main Authors: Bomfim, Thiago, Torres, Maria Joana, Varandas, Paulo
Format: Article
Language:English
Subjects:
Gluing orbit property
Partial hyperbolicity
Recurrence
Specification
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 article is a follow up of our recent works [7,8], and here we discuss the relation between the gluing orbit property and partial hyperbolicity. First we prove that a partially hyperbolic diffeomorphism with two saddles with different index, and such that the stable manifold of one of these saddles coincides with the strongly stable leaf does not satisfy the gluing orbit property. In particular, the examples of C1-robustly transitive diffeomorphisms introduced by Mañé [20] do not satisfy the gluing orbit property. We also construct some families of partially hyperbolic skew-products satisfying the gluing orbit property and derive some estimates on their quantitative recurrence.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.09.040