Outputs (3)

A dichotomy in orbit growth for commuting automorphisms (2010)
Journal Article
Miles, R., & Ward, T. (2010). A dichotomy in orbit growth for commuting automorphisms. Journal of the London Mathematical Society, 81(3), 715-726. https://doi.org/10.1112/jlms/jdq010

We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts, and those... Read More about A dichotomy in orbit growth for commuting automorphisms.

Dirichlet series for finite combinatorial rank dynamics (2010)
Journal Article
Everest, G., Miles, R., Stevens, S., & Ward, T. (2010). Dirichlet series for finite combinatorial rank dynamics. Transactions of the American Mathematical Society, 362(01), 199-227. https://doi.org/10.1090/s0002-9947-09-04962-9

We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to hav... Read More about Dirichlet series for finite combinatorial rank dynamics.

Planar dynamical systems with pure Lebesgue diffraction spectrum (2010)
Journal Article
Baake, M., & Ward, T. (2010). Planar dynamical systems with pure Lebesgue diffraction spectrum. Journal of Statistical Physics, 140(1), 90-102. https://doi.org/10.1007/s10955-010-9984-x

We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the presence... Read More about Planar dynamical systems with pure Lebesgue diffraction spectrum.