Volume 20, issue 1 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Boundary distance, lens maps and entropy of geodesic flows of Finsler metrics

Dmitri Burago and Sergei Ivanov

Geometry & Topology 20 (2016) 469–490

We show that a small perturbation of the boundary distance function of a simple Finsler metric on the n–disc is also the boundary distance function of some Finsler metric. (Simple metrics form an open class containing all flat metrics.) The lens map is a map that sends the exit vector to the entry vector as a geodesic crosses the disc. We show that a small perturbation of a lens map of a simple Finsler metric is in its turn the lens map of some Finsler metric. We use this result to construct a smooth perturbation of the metric on the standard 4–dimensional sphere to produce positive metric entropy of the geodesic flow. Furthermore, this flow exhibits local generation of metric entropy; that is, positive entropy is generated in arbitrarily small tubes around one trajectory.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address 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:

Finsler metric, boundary distance, lens map, scattering relation, Hamiltonian flow, perturbation, metric entropy
Mathematical Subject Classification 2010
Primary: 53C60, 37A35, 37J40
Received: 7 August 2014
Revised: 8 October 2014
Accepted: 8 October 2014
Published: 29 February 2016
Proposed: Leonid Polterovich
Seconded: Jean-Pierre Otal, Gang Tian
Dmitri Burago
Department of Mathematics
Pennsylvania State University
University Park
State College, PA 16802
Sergei Ivanov
St. Petersburg Department of Steklov Mathematical Institute
Russian Academy of Sciences
Fontanka 27
St. Petersburg 191023