P. D'Ambros
Dynamical systems arising from elliptic curves
D'Ambros, P.; Everest, G.; Miles, R.; Ward, T.
Authors
G. Everest
R. Miles
T. Ward
Abstract
We exhibit a family of dynamical systems arising from rational points on elliptic curves in an attempt to mimic the familiar toral automorphisms. At the non-archimedean primes, a continuous map is constructed on the local elliptic curve whose topological entropy is given by the local canonical height. Also, a precise formula for the periodic points is given. There follows a discussion of how these local results may be glued together to give a map on the adelic curve. We are able to give a map whose entropy is the global canonical height and whose periodic points are counted asymptotically by the real division polynomial (although the archimedean component of the map is artificial). Finally, we set out a precise conjecture about the existence of elliptic dynamical systems and discuss a possible connection with mathematical physics.
Citation
D'Ambros, P., Everest, G., Miles, R., & Ward, T. (2000). Dynamical systems arising from elliptic curves. Colloquium Mathematicum, 84/85(1), 95-107
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2000 |
Deposit Date | Oct 12, 2012 |
Publicly Available Date | Oct 17, 2012 |
Journal | Colloquium Mathematicum |
Print ISSN | 0010-1354 |
Electronic ISSN | 1730-6302 |
Publisher | Instytut Matematyczny |
Peer Reviewed | Peer Reviewed |
Volume | 84/85 |
Issue | 1 |
Pages | 95-107 |
Public URL | https://durham-repository.worktribe.com/output/1472983 |
Publisher URL | http://journals.impan.gov.pl/Publ/cm84-85ind.html |
Files
Published Journal Article
(167 Kb)
PDF
You might also like
An introduction to Number Theory
(2011)
Book
An Introduction to Number Theory
(2005)
Book
Recurrence Sequences
(2003)
Book
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search