The Hasse-Weil Bound and Integrability Detection in Rational Maps

DOI

10.2991/jnmp.2003.10.s2.15How to use a DOI?

Abstract

We reduce planar measure-preserving rational maps over finite fields, and study their discrete dynamics. We show that application to the orbit analysis over these fields of the Hasse-Weil bound for the number of points on an algebraic curve gives a strong indication of the existence of an integral for the map. Moreover, the method is ideally suited to separating near-integrability from genuine integrability.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - John A.G. Roberts
AU  - Danesh Jogia
AU  - Franco Vivaldi
PY  - 2003
DA  - 2003/12/01
TI  - The Hasse-Weil Bound and Integrability Detection in Rational Maps
JO  - Journal of Nonlinear Mathematical Physics
SP  - 166
EP  - 180
VL  - 10
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.s2.15
DO  - 10.2991/jnmp.2003.10.s2.15
ID  - Roberts2003
ER  -