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Dynamical systems arising from elliptic curves

D'Ambros, P.; Everest, G.; Miles, R.; Ward, T.

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Authors

P. D'Ambros

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 Mar 29, 2024
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
Publisher URL http://journals.impan.gov.pl/Publ/cm84-85ind.html

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