Outputs (7)

Homogeneous dynamics: a study guide (2015)
Book Chapter
Einsiedler, M., & Ward, T. (2015). Homogeneous dynamics: a study guide. In S. Cheng, L. Ji, Y. Poon, J. Xiao, L. Yang, & S. Yau (Eds.), Introduction to modern mathematics (171-202). International Press of Boston

These notes give a summary of the course ‘Ergodic theory and Applications in Number Theory’ at the Summer School in Modern Mathematics at the Tsinghua University in Beijing, June 23–27 (2013). As in the Summer school, we will need to be brief at time... Read More about Homogeneous dynamics: a study guide.

Dynamical invariants for group automorphisms (2015)
Book Chapter
Miles, R., Staines, M., & Ward, T. (2015). Dynamical invariants for group automorphisms. In S. Bhattacharya, T. Das, A. Ghosh, & R. Shah (Eds.), Recent trends in ergodic theory and dynamical systems : international conference in honor of S.G. Dani's 65th birthday, December 26-29, 2012, Vadodara, India (231-258). American Mathematical Society. https://doi.org/10.1090/conm/631/12606

We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of one-dimensional solenoids, a complete description is given and the pro... Read More about Dynamical invariants for group automorphisms.

Ergodic theory: interactions with combinatorics and number theory (2009)
Book Chapter
Ward, T. (2009). Ergodic theory: interactions with combinatorics and number theory. In R. Meyers (Ed.), Encyclopedia of complexity and systems science (3040-3053). Springer Verlag. https://doi.org/10.1007/springerreference_60353

Mixing and tight polyhedra (2006)
Book Chapter
Ward, T. (2006). Mixing and tight polyhedra. In D. Denteneer, F. den Hollander, & E. Verbitskiy (Eds.), Dynamics & stochastics (169-175). Institute of Mathematical Statistics. https://doi.org/10.1214/074921706000000194

Orbit counting with an isometric direction (2005)
Book Chapter
Everest, G., Stangoe, V., & Ward, T. (2005). Orbit counting with an isometric direction. In S. Kolyada, Y. Manin, & T. Ward (Eds.), Algebraic and topological dynamics (293-302). American Mathematical Society. https://doi.org/10.1090/conm/385/07202

Morphic heights and periodic points (2004)
Book Chapter
Einsiedler, M., Everest, G., & Ward, T. (2004). Morphic heights and periodic points. In D. Chudnovsky, G. Chudnovsky, & M. Nathanson (Eds.), Number theory : New York seminar 2003 (167-177). Springer Verlag

An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic height is expre... Read More about Morphic heights and periodic points.

A higher-rank Mersenne problem (2002)
Book Chapter
Everest, G., Rogers, P., & Ward, T. (2002). A higher-rank Mersenne problem. In C. Fieker, & D. Kohel (Eds.), Algorithmic number theory (95-107). Springer Verlag. https://doi.org/10.1007/3-540-45455-1_8

The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue... Read More about A higher-rank Mersenne problem.