# 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.

### 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 Dynamics*Dynamics 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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