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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.

Useful links

ORCID page
Google scholar page
AMS author profile

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
View abstract