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Additive cellular automata and volume growth (2000)
Journal Article
Ward, T. (2000). Additive cellular automata and volume growth. Entropy, 2(3), 142-167. https://doi.org/10.3390/e2030142

A class of dynamical systems associated to rings of S-integers in rational function fields is described. General results about these systems give a rather complete description of the well-known dynamics in one-dimensional additive cellular automata w... Read More about Additive cellular automata and volume growth.

Dynamical zeta functions for typical extensions of full shifts (1999)
Journal Article
Ward, T. (1999). Dynamical zeta functions for typical extensions of full shifts. Finite Fields and Their Applications, 5(3), 232-239. https://doi.org/10.1006/ffta.1999.0250

We consider a family of isometric extensions of the full shift on p symbols (for p a prime) parametrised by a probability space. Using Heath-Brown's work on the Artin conjecture, it is shown that for all but two primes p the set of limit points of th... Read More about Dynamical zeta functions for typical extensions of full shifts.

Almost all S-integer dynamical systems have many periodic points (1998)
Journal Article
Ward, T. (1998). Almost all S-integer dynamical systems have many periodic points. Ergodic Theory and Dynamical Systems, 18(2), 471-486. https://doi.org/10.1017/s0143385798113378

We show that for almost every ergodic S-integer dynamical system the radius of convergence of the dynamical zeta function is no larger than exp(-[1/2]htop) < 1. In the arithmetic case almost every zeta function is irrational. We conjecture that for a... Read More about Almost all S-integer dynamical systems have many periodic points.

Entropy bounds for endomorphisms commuting with K actions (1998)
Journal Article
Morris, G., & Ward, T. (1998). Entropy bounds for endomorphisms commuting with K actions. Israel Journal of Mathematics, 106(1), 1-12. https://doi.org/10.1007/bf02773458

Shereshevsky has shown that a shift-commuting homeomorphism from the two-dimensional full shift to itself cannot be expansive, and asked if such a homeomorphism can have finite positive entropy. We formulate an algebraic analogue of this problem, and... Read More about Entropy bounds for endomorphisms commuting with K actions.

An uncountable family of group automorphisms, and a typical member (1997)
Journal Article
Ward, T. (1997). An uncountable family of group automorphisms, and a typical member. Bulletin of the London Mathematical Society, 29(5), 577-584. https://doi.org/10.1112/s0024609397003330

We describe an uncountable family of compact group automorphisms with entropy log2. Each member of the family has a distinct dynamical zeta function, and the members are parametrised by a probability space. A positive proportion of the members have p... Read More about An uncountable family of group automorphisms, and a typical member.

S-integer dynamical systems: periodic points (1997)
Journal Article
Chothi, V., Everest, G., & Ward, T. (1997). S-integer dynamical systems: periodic points. Journal für die reine und angewandte Mathematik, 1997(489), 99-132. https://doi.org/10.1515/crll.1997.489.99

We associate via duality a dynamical system to each pair (R_S,x), where R_S is the ring of S-integers in an A-field k, and x is an element of R_S\{0}. These dynamical systems include the circle doubling map, certain solenoidal and toral endomorphisms... Read More about S-integer dynamical systems: periodic points.