# School of Mathematics

## Prof Thomas B Ward

Professor in Pure Mathematics
Pure Mathematics

### Keywords

Ergodic theory
Entropy
Number theory
Diophantine approximation
Recurrence relations
Zeta functions

## Research interests

My research area is ergodic theory and dynamical systems, with a particular emphasis on dynamical systems of algebraic origin and interactions with number theory. A particular interest is how relatively simple questions in dynamical systems can involve subtle problems in number theory.

## Publications

Luca F, Ward T An elliptic sequence is not a sampled linear recurrence sequence New York Journal of Mathematics, 22, 1319-1338, 2016
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Einsiedler M; Ward T Diophantine Problems and Homogeneous DynamicsDynamics and analytic number theory, 258-288 2016
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Stevens S, Ward T, Zegowitz S Halving dynamical systems Contemporary Mathematics, 669, 298-311, 2016
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Miles R, Ward T Directional uniformities, periodic points, and entropy Discrete and Continuous Dynamical Systems - Series B, 20, 3525-3545, 2015
DOI:10.3934/dcdsb.2015.20.3525
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Einsiedler M, Ward T Homogeneous dynamics: a study guide In Introduction to modern mathematics, 33, 171-201, 2015
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Miles R, Staines M, Ward TB Dynamical invariants for group automorphisms In Recent Trends in Ergodic Theory and Dynamical Systems, 631, 231-258, 2015
DOI:10.1090/conm/631/12606
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Bell J, Miles R, Ward T Towards a Pólya–Carlson dichotomy for algebraic dynamics Indagationes Mathematicae, 25, 652-668, 2014
DOI:10.1016/j.indag.2014.04.005
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Bell J, Miles R, Ward T Towards a Pólya-Carlson dichotomy for algebraic dynamics Indagationes Mathematicae, 25, 652-668, 2014
DOI:10.1016/j.indag.2014.04.005
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Pakapongpun A, Ward T Orbits for products of maps Thai Journal of Mathematics, 12, 33-44, 2014
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Ward T Graham Everest 1957–2010 Bulletin of the London Mathematical Society, 45, 1110-1118, 2013
DOI:10.1112/blms/bdt053

Ward TB Chaos and fractals. An elementary introduction [book review, Oxford Univ. Press, Oxford, 2012] European Mathematical Society. Newsletter, 64-65, 2013

Baier S, Jaidee S, Stevens S, Ward T Automorphisms with exotic orbit growth Acta Arithmetica, 158, 173-197, 2013
DOI:10.4064/aa158-2-5
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Ward T Ergodic theory: interactions with combinatorics and number theory In Mathematics of complexity and dynamical systems. Vols. 1–3, 313-326, 2012
DOI:10.1007/978-1-4614-1806-1_20

Everest G, Ward T A repulsion motif in Diophantine equations American Mathematical Monthly, 118, 584-598, 2011
DOI:10.4169/amer.math.monthly.118.07.584

Flatters A, Ward T A polynomial Zsigmondy theorem Journal of Algebra, 343, 138-142, 2011
DOI:10.1016/j.jalgebra.2011.07.010

Miles R, Ward T A directional uniformity of periodic point distribution and mixing Discrete and Continuous Dynamical Systems. Series A, 30, 1181-1189, 2011
DOI:10.3934/dcds.2011.30.1181

Jaidee S, Stevens S, Ward T Mertens’ theorem for toral automorphisms Proceedings of the American Mathematical Society, 139, 1819-1824, 2011
DOI:10.1090/S0002-9939-2010-10632-9

Einsiedler M; Ward T Ergodic theory with a view towards number theory. 259, Springer-Verlag London, Ltd. London 2011
DOI:10.1007/978-0-85729-021-2

Dynamical numbers—interplay between dynamical systems and number theory, xii+242-xii+242 2010
DOI:10.1090/conm/532

Baake M, Ward T Planar dynamical systems with pure Lebesgue diffraction spectrum Journal of Statistical Physics, 140, 90-102, 2010
DOI:10.1007/s10955-010-9984-x

Miles R, Ward T A dichotomy in orbit growth for commuting automorphisms Journal of the London Mathematical Society. Second Series, 81, 715-726, 2010
DOI:10.1112/jlms/jdq010

Everest G, Miles R, Stevens S, Ward T Dirichlet series for finite combinatorial rank dynamics Transactions of the American Mathematical Society, 362, 199-227, 2010
DOI:10.1090/S0002-9947-09-04962-9

Everest G, Röttger C, Ward T The continuing story of zeta The Mathematical Intelligencer, 31, 13-17, 2009
DOI:10.1007/s00283-009-9053-y

Ward T, Yayama Y Markov partitions reflecting the geometry of $\times 2,\times 3$ Discrete and Continuous Dynamical Systems. Series A, 24, 613-624, 2009
DOI:10.3934/dcds.2009.24.613

Pakapongpun A, Ward T Functorial orbit counting Journal of Integer Sequences, 12, Article 09.2.4-20, 2009

Miles R, Ward T Orbit-counting for nilpotent group shifts Proceedings of the American Mathematical Society, 137, 1499-1507, 2009
DOI:10.1090/S0002-9939-08-09649-4

Phillips J, Ward T, Montgomery PQ Variations in Posttonsillectomy Hemorrhage Rates Are Scale Invariant The Laryngoscope, 118, 1096-1098, 2008
DOI:10.1097/MLG.0b013e3181672277

Miles R, Ward T Uniform periodic point growth in entropy rank one Proceedings of the American Mathematical Society, 136, 359-365, 2008
DOI:10.1090/S0002-9939-07-09018-1

Everest G, Miles R, Stevens S, Ward T Orbit-counting in non-hyperbolic dynamical systems Journal für die Reine und Angewandte Mathematik. [Crelle’s Journal], 608, 155-182, 2007
DOI:10.1515/CRELLE.2007.056

Everest G, Stevens S, Tamsett D, Ward T Primes generated by recurrence sequences American Mathematical Monthly, 114, 417-431, 2007

Ward T Mixing and tight polyhedra In Dynamics&stochastics, 48, 169-175, 2006
DOI:10.1214/074921706000000194

Miles R, Ward T Periodic point data detects subdynamics in entropy rank one Ergodic Theory and Dynamical Systems, 26, 1913-1930, 2006
DOI:10.1017/S014338570600054X

Miles R, Ward T Mixing actions of the rationals Ergodic Theory and Dynamical Systems, 26, 1905-1911, 2006
DOI:10.1017/S0143385706000356

Everest G, Mclaren G, Ward T Primitive divisors of elliptic divisibility sequences Journal of Number Theory, 118, 71-89, 2006
DOI:10.1016/j.jnt.2005.08.002

Algebraic and topological dynamics, xii+364-xii+364 2005
DOI:10.1090/conm/385

Everest G, Stangoe V, Ward T Orbit counting with an isometric direction In Algebraic and topological dynamics, 385, 293-302, 2005
DOI:10.1090/conm/385/07202

Einsiedler M, Ward T Isomorphism rigidity in entropy rank two Israel Journal of Mathematics, 147, 269-284, 2005
DOI:10.1007/BF02785368

Einsiedler M, Ward T Entropy geometry and disjointness for zero-dimensional algebraic actions Journal für die Reine und Angewandte Mathematik, 584, 195-214, 2005
DOI:10.1515/crll.2005.2005.584.195

Everest G; Ward T An introduction to number theory. 232, Springer-Verlag London, Ltd. London 2005

Bhattacharya S, Ward T Finite entropy characterizes topological rigidity on connected groups Ergodic Theory and Dynamical Systems, 25, 365-373, 2005
DOI:10.1017/S0143385704000501

Ward T Group automorphisms with few and with many periodic points Proceedings of the American Mathematical Society, 133, 91-96 (electronic), 2005
DOI:10.1090/S0002-9939-04-07626-9

Einsiedler M, Everest G, Ward T Periodic points for good reduction maps on curves Geometriae Dedicata, 106, 29-41, 2004
DOI:10.1023/B:GEOM.0000033838.15992.72

Einsiedler M, Everest G, Ward T Morphic heights and periodic points In Number theory (New York, 2003), 167-177, 2004

Everest G; van der Poorten A; Shparlinski I; Ward T Recurrence sequences. 104, American Mathematical Society, Providence, RI 2003
DOI:10.1090/surv/104

Einsiedler M, Ward T Asymptotic geometry of non-mixing sequences Ergodic Theory and Dynamical Systems, 23, 75-85, 2003
DOI:10.1017/S0143385702000950

Everest G, Rogers P, Ward T A higher-rank Mersenne problem In Algorithmic number theory (Sydney, 2002), 2369, 95-107, 2002
DOI:10.1007/3-540-45455-1_8

Everest G, van der Poorten AJ, Puri Y, Ward T Integer sequences and periodic points Journal of Integer Sequences, 5, Article 02.2.3-10, 2002

Everest G, Ward T Primes in divisibility sequences Cubo Matemática Educacional, 3, 245-259, 2001

Einsiedler M, Everest G, Ward T Entropy and the canonical height Journal of Number Theory, 91, 256-273, 2001
DOI:10.1006/jnth.2001.2682

Puri Y, Ward T Arithmetic and growth of periodic orbits Journal of Integer Sequences, 4, Article 01.2.1-18, 2001

Einsiedler M, Lind D, Miles R, Ward T Expansive subdynamics for algebraic $\Bbb Z^d$-actions Ergodic Theory and Dynamical Systems, 21, 1695-1729, 2001
DOI:10.1017/S014338570100181X

Puri Y, Ward T A dynamical property unique to the Lucas sequence The Fibonacci Quarterly. The Official Journal of the Fibonacci Association, 39, 398-402, 2001

Einsiedler M, Everest G, Ward T Primes in elliptic divisibility sequences LMS Journal of Computation and Mathematics, 4, 1-13 (electronic), 2001
DOI:10.1112/S1461157000000772

Ward TB Additive cellular automata and volume growth Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 2, 142-167 (electronic), 2000
DOI:10.3390/e2030142

Everest G, Ward T The canonical height of an algebraic point on an elliptic curve New York Journal of Mathematics, 6, 331-342 (electronic), 2000

Einsiedler M, Everest G, Ward T Primes in sequences associated to polynomials (after Lehmer) LMS Journal of Computation and Mathematics, 3, 125-139 (electronic), 2000
DOI:10.1112/S1461157000000255

D Ambros P, Everest G, Miles R, Ward T Dynamical systems arising from elliptic curves Colloquium Mathematicum, 84/85, 95-107, 2000

Einsiedler M, Ward T Fitting ideals for finitely presented algebraic dynamical systems Aequationes Mathematicae, 60, 57-71, 2000
DOI:10.1007/s000100050135

Ward T Dynamical zeta functions for typical extensions of full shifts Finite Fields and their Applications, 5, 232-239, 1999
DOI:10.1006/ffta.1999.0250

Everest G; Ward T Heights of polynomials and entropy in algebraic dynamics. Springer-Verlag London, Ltd. London 1999
DOI:10.1007/978-1-4471-3898-3

Everest G, Ward T A dynamical interpretation of the global canonical height on an elliptic curve Experimental Mathematics, 7, 305-316, 1998

Morris G, Ward T Entropy bounds for endomorphisms commuting with $K$ actions Israel Journal of Mathematics, 106, 1-11, 1998
DOI:10.1007/BF02773458

Ward T A family of Markov shifts (almost) classified by periodic points Journal of Number Theory, 71, 1-11, 1998
DOI:10.1006/jnth.1998.2242

Ward TB Almost all $S$-integer dynamical systems have many periodic points Ergodic Theory and Dynamical Systems, 18, 471-486, 1998
DOI:10.1017/S0143385798113378

Morris G, Ward T A note on mixing properties of invertible extensions Acta Mathematica Universitatis Comenianae. New Series, 66, 307-311, 1997

Ward T Three results on mixing shapes New York Journal of Mathematics, 3A, 1-10 (electronic), 1997

Chothi V, Everest G, Ward T $S$-integer dynamical systems: periodic points Journal für die Reine und Angewandte Mathematik, 489, 99-132, 1997

Ward T An uncountable family of group automorphisms, and a typical member The Bulletin of the London Mathematical Society, 29, 577-584, 1997
DOI:10.1112/S0024609397003330

Ward T Rescaling of Markov shifts Acta Mathematica Universitatis Comenianae. New Series, 65, 149-157, 1996

Chothi V, Everest G, Ward T Oriented local entropies for expansive actions by commuting automorphisms Israel Journal of Mathematics, 93, 281-301, 1996
DOI:10.1007/BF02761107

Ward T Additive relations in fields: an entropy approach Journal of Number Theory, 53, 137-143, 1995
DOI:10.1006/jnth.1995.1082

Ward T Automorphisms of $\bold Z^d$-subshifts of finite type Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series, 5, 495-504, 1994
DOI:10.1016/0019-3577(94)90020-5

Ward TB An algebraic obstruction to isomorphism of Markov shifts with group alphabets The Bulletin of the London Mathematical Society, 25, 240-246, 1993
DOI:10.1112/blms/25.3.240

Schmidt K, Ward T Mixing automorphisms of compact groups and a theorem of Schlickewei Inventiones Mathematicae, 111, 69-76, 1993
DOI:10.1007/BF01231280

Ward TB The Bernoulli property for expansive $\bold Z^2$ actions on compact groups Israel Journal of Mathematics, 79, 225-249, 1992
DOI:10.1007/BF02808217

Ward T, Zhang Q The Abramov-Rokhlin entropy addition formula for amenable group actions Monatshefte für Mathematik, 114, 317-329, 1992
DOI:10.1007/BF01299386

Ward TB Periodic points for expansive actions of $\bf Z^d$ on compact abelian groups The Bulletin of the London Mathematical Society, 24, 317-324, 1992
DOI:10.1112/blms/24.4.317

Ward TB Almost block independence for the three dot $\bf Z^2$ dynamical system Israel Journal of Mathematics, 76, 237-256, 1991
DOI:10.1007/BF02782855

Lind D, Schmidt K, Ward T Mahler measure and entropy for commuting automorphisms of compact groups Inventiones Mathematicae, 101, 593-629, 1990
DOI:10.1007/BF01231517

Lind DA, Ward T Automorphisms of solenoids and $p$-adic entropy Ergodic Theory and Dynamical Systems, 8, 411-419, 1988
DOI:10.1017/S0143385700004545

Miles R, Ward TB The dynamical zeta function for commuting automorphisms of zero-dimensional groups Ergodic Theory and Dynamical Systems
DOI:10.1017/etds.2016.77
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