### Dynamical systems arising from elliptic curves, by P. D'Ambros, G. Everest, R. Miles, T. Ward

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.

P. D'Ambros, G. Everest, R. Miles, T. Ward <g.everest@uea.ac.uk>