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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.