Outputs (65)

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.

Book review: "Automorphisms and equivalence relations in topological dynamics" (2015)
Journal Article
Ward, T. (2015). Book review: "Automorphisms and equivalence relations in topological dynamics". Proceedings of the Edinburgh Mathematical Society, 807-808. https://doi.org/10.1017/s0013091515000607

Towards a Pólya–Carlson dichotomy for algebraic dynamics (2014)
Journal Article
Bell, J., Miles, R., & Ward, T. (2014). Towards a Pólya–Carlson dichotomy for algebraic dynamics. Indagationes Mathematicae, 25(4), 652-668. https://doi.org/10.1016/j.indag.2014.04.005

We present results and background rationale in support of a Pólya–Carlson dichotomy between rationality and a natural boundary for the analytic behaviour of dynamical zeta functions of compact 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.

Obituary: Graham Everest 1957-2010 (2013)
Journal Article
Ward, T. (2013). Obituary: Graham Everest 1957-2010. Bulletin of the London Mathematical Society, 45(5), 1110-1118. https://doi.org/10.1112/blms/bdt053

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.

A polynomial Zsigmondy theorem (2011)
Journal Article
Flatters, A., & Ward, T. (2011). A polynomial Zsigmondy theorem. Journal of Algebra, 343(1), 138-142. https://doi.org/10.1016/j.jalgebra.2011.07.010

We find an analogue of the primitive divisor results of Bang and Zsigmondy in polynomial rings.

A directional uniformity of periodic point distribution and mixing (2011)
Journal Article
Miles, R., & Ward, T. (2011). A directional uniformity of periodic point distribution and mixing. Discrete and Continuous Dynamical Systems - Series A, 30(4), 1181-1189. https://doi.org/10.3934/dcds.2011.30.1181

For mixing Z^d-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown... Read More about A directional uniformity of periodic point distribution and mixing.

A repulsion motif in Diophantine equations (2011)
Journal Article
Everest, G., & Ward, T. (2011). A repulsion motif in Diophantine equations. The American Mathematical Monthly, 118(7), 584-598. https://doi.org/10.4169/amer.math.monthly.118.07.584

Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a non-singular plane cubic equation has... Read More about A repulsion motif in Diophantine equations.

Mertens' theorem for toral automorphisms (2011)
Journal Article
Jaidee, S., Stevens, S., & Ward, T. (2011). Mertens' theorem for toral automorphisms. Proceedings of the American Mathematical Society, 139(05), 1819-1824. https://doi.org/10.1090/s0002-9939-2010-10632-9

A dynamical Mertens' theorem for ergodic toral automorphisms with error term O(N^{-1}) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer, periodic orbit... Read More about Mertens' theorem for toral automorphisms.