Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 4
Volume 13, Issue 3
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN 2996-220X (online)
ISSN 2996-2196 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
$k$-divergent lattices

Guy Lachman, Anurag Rao, Uri Shapira and Yuval Yifrach
Vol. 13 (2024), No. 3, 207–224
DOI: 10.2140/cnt.2024.13.207
Abstract

We introduce a novel concept in topological dynamics, referred to as k-divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogeneous Diophantine approximations, we investigate this notion in the dynamical system given by a certain flow on the space of unimodular lattices in ℝd . Our main result is the existence of k-divergent lattices for any k ≥ 0. In fact, we utilize the emerging theory of parametric geometry of numbers and calculate the Hausdorff dimension of the set of k-divergent lattices.

PDF Access Denied

We have not been able to recognize your IP address 3.138.135.4 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
dynamical systems, Diophantine approximation
Mathematical Subject Classification
Primary: 11J83, 37B02
Milestones
Received: 23 February 2024
Accepted: 9 July 2024
Published: 16 August 2024
Authors
Guy Lachman
Tel Aviv University
Tel Aviv
Israel
Anurag Rao
BICMR
Peking University
Beijing
China
Uri Shapira
Israel Institute of Technology - Technion
Haifa
Israel
Yuval Yifrach
Israel Institute of Technology - Technion
Haifa
Israel
© 2024 MSP (Mathematical Sciences Publishers).