Outputs (3)

Mixing actions of the rationals (2006)
Journal Article
Miles, R., & Ward, T. (2006). Mixing actions of the rationals. Ergodic Theory and Dynamical Systems, 26(6), 1905-1911. https://doi.org/10.1017/s0143385706000356

We study mixing properties of algebraic actions of Q^d, showing in particular that prime mixing Q^d-actions on connected groups are mixing of all orders, as is the case for Z^d-actions. This is shown using a uniform result on the solution of S-unit e... Read More about Mixing actions of the rationals.

Periodic point data detects subdynamics in entropy rank one (2006)
Journal Article
Miles, R., & Ward, T. (2006). Periodic point data detects subdynamics in entropy rank one. Ergodic Theory and Dynamical Systems, 26(6), 1913-1930. https://doi.org/10.1017/s014338570600054x

A framework for understanding the geometry of continuous actions of Z^d was developed by Boyle and Lind using the notion of expansive behaviour along lower-dimensional subspaces. For algebraic Zd-actions of entropy rank one, the expansive subdynamics... Read More about Periodic point data detects subdynamics in entropy rank one.

Primitive divisors of elliptic divisibility sequences (2006)
Journal Article
Everest, G., McLaren, G., & Ward, T. (2006). Primitive divisors of elliptic divisibility sequences. Journal of Number Theory, 118(1), 71-89. https://doi.org/10.1016/j.jnt.2005.08.002

Silverman proved the analogue of Zsigmondy's Theorem for elliptic divisibility sequences. For elliptic curves in global minimal form, it seems likely this result is true in a uniform manner. We present such a result for certain infinite families of c... Read More about Primitive divisors of elliptic divisibility sequences.