Vol. 12, No. 7, 2018

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

Volume 12
Issue 10, 2237–2514
Issue 9, 2033–2235
Issue 8, 1823–2032
Issue 7, 1559–1821
Issue 6, 1311–1557
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

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
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Other MSP Journals
Arithmetic degrees and dynamical degrees of endomorphisms on surfaces

Yohsuke Matsuzawa, Kaoru Sano and Takahiro Shibata

Vol. 12 (2018), No. 7, 1635–1657

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.

arithmetic degree, dynamical degrees, arithmetic dynamics
Mathematical Subject Classification 2010
Primary: 14G05
Secondary: 11G35, 11G50, 37P05, 37P15, 37P30
Received: 20 March 2017
Revised: 5 April 2018
Accepted: 20 June 2018
Published: 27 October 2018
Yohsuke Matsuzawa
Graduate school of Mathematical Sciences
University of Tokyo
Komaba, Tokyo
Kaoru Sano
Department of Mathematics, Faculty of Science
Kyoto University
Takahiro Shibata
Department of Mathematics, Faculty of Science
Kyoto University