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Directional uniformities, periodic points, and entropy (2015)
Journal Article
Miles, R., & Ward, T. (2015). Directional uniformities, periodic points, and entropy. Discrete and Continuous Dynamical Systems - Series B, 20(10), 3525-3545. https://doi.org/10.3934/dcdsb.2015.20.3525

Dynamical systems generated by d≥2 commuting homeomorphisms (topological Z d -actions) contain within them structures on many scales, and in particular contain many actions of Z k for 1≤k≤d . Familiar dynamical invariants for homeomorphisms, like ent... Read More about Directional uniformities, periodic points, and entropy.

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.

Orbits for products of maps (2014)
Journal Article
Pakapongpun, A., & Ward, T. (2014). Orbits for products of maps. Thai Journal of Mathematics, 12(1), 33-44

We study the behaviour of the dynamical zeta function and the orbit Dirichlet series for products of maps. The behaviour under products of the radius of convergence for the zeta function, and the abscissa of convergence for the orbit Dirichlet series... Read More about Orbits for products of maps.

Automorphisms with exotic orbit growth (2013)
Journal Article
Baier, S., Jaidee, S., Stevens, S., & Ward, T. (2013). Automorphisms with exotic orbit growth. Acta Arithmetica, 158, 173-197. https://doi.org/10.4064/aa158-2-5

The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on... Read More about Automorphisms with exotic orbit growth.