Vol. 12, No. 7, 2018

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

Volume 13
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Other MSP Journals
This article is available for purchase or by subscription. See below.
Arithmetic degrees and dynamical degrees of endomorphisms on surfaces

Yohsuke Matsuzawa, Kaoru Sano and Takahiro Shibata

Vol. 12 (2018), No. 7, 1635–1657
Abstract

For a dominant rational self-map on a smooth projective variety defined over a number field, Kawaguchi and Silverman conjectured that the (first) dynamical degree is equal to the arithmetic degree at a rational point whose forward orbit is well-defined and Zariski dense. We prove this conjecture for surjective endomorphisms on smooth projective surfaces. For surjective endomorphisms on any smooth projective varieties, we show the existence of rational points whose arithmetic degrees are equal to the dynamical degree. Moreover, if the map is an automorphism, there exists a Zariski dense set of such points with pairwise disjoint orbits.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 34.239.158.107 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
arithmetic degree, dynamical degrees, arithmetic dynamics
Mathematical Subject Classification 2010
Primary: 14G05
Secondary: 11G35, 11G50, 37P05, 37P15, 37P30
Milestones
Received: 20 March 2017
Revised: 5 April 2018
Accepted: 20 June 2018
Published: 27 October 2018
Authors
Yohsuke Matsuzawa
Graduate school of Mathematical Sciences
University of Tokyo
Komaba, Tokyo
Japan
Kaoru Sano
Department of Mathematics, Faculty of Science
Kyoto University
Japan
Takahiro Shibata
Department of Mathematics, Faculty of Science
Kyoto University
Japan