Prof. Thomas Ward

List of publications by Tom Ward

Preprints : Research papers : Books : Edited proceedings : Surveys and essays : Book reviews : Some preprints at the arXiv

Preprints

S. Baier, S. Jaidee, S. Stevens & T. Ward; "Automorphisms with exotic orbit growth" (arXiv:1201.4503, submitted 24 January 2012)

A. Pakapongpun & T. Ward; "Orbits for products of maps" (arXiv:1001.0314, submitted 7 November 2010)

Research papers (accepted or appeared; copyright is held by the publishers in most cases)

[61] A. Flatters & T. Ward; "A polynomial Zsigmondy theorem", Journal of Algebra, 343 (1), 138-142 (2011). (arXiv:1002.4829, DOI)

[60] G. Everest & T. Ward; "The repulsion motif in Diophantine equations", Amer. Math. Monthly, 118, No. 7, 584-598 (2011). (arXiv:1005.0315)

[59] R. Miles & T. Ward; "A directional uniformity of periodic point distribution and mixing", Discrete and Continuous Dynamical Systems, 30 (4), 1181-1189 (2011). (arXiv:1001.0390, DOI)

[58] S. Jaidee, S. Stevens & T. Ward; "Mertens' theorem for toral automorphisms", Proc. Amer. Math. Soc., 139, 1819-1824 (2011). (arXiv:0801.2082, DOI, GS)

[57] M. Baake & T. Ward; "Planar dynamical systems with pure Lebesgue diffraction spectrum", Journal of Statistical Physics, 140, No. 1, 90-102 (2010). (arXiv:1003.1536, DOI, GS)

[56] R. Miles & T. Ward; "A dichotomy in orbit-growth for commuting automorphisms", J. London Math. Soc., 81, 715-726 (2010). (arXiv:0904.3492, DOI, GS, Zbl.1193.37006)

[55] G. Everest, C. Röttger & T. Ward; "The continuing story of zeta", Math. Intelligencer, 31, No. 3, 13-17 (2009) (arXiv:math/0610108v2, DOI, GS, wordle)

[54] Apisit Pakapongpun & Thomas Ward; "Functorial orbit counting", Journal of Integer Sequences, 12:Article 09.2.4, 2009. (arXiv:0901.2646, GS, MR2010c:37044)

[53] G. Everest, R. Miles, S. Stevens & T. Ward; "Dirichlet series for finite combinatorial rank dynamics", Trans. Amer. Math. Soc. 362, 199-227 (2010) (arXiv:0705.1067v2, DOI, GS, Zbl.1195.37014)

[52] T. Ward & Y. Yayama; "Markov partitions reflecting the geometry of x2,x3", Discrete and Continuous Dynamical Systems 24, No. 2, 613-624 (2009) (arXiv:0801.1195, DOI, GS, MR2010c:22008, Zbl.1172.22004)

[51] R. Miles & T. Ward; "Orbit-counting for nilpotent group shifts", Proc. Amer. Math. Soc. 137, 1499-1507 (2009) (Abstract, arXiv:0706.3630, DOI, GS, MR2010b:37011, Zbl.1160.22005)

[50] J. Phillips, T. Ward & P. Q. Montgomery, "Variations in posttonsillectomy haemorrhage rates are scale-invariant", The Laryngoscope, 118, issue 6, 1096-1098 (2008). (DOI)

[49] R. Miles & T. Ward; "Uniform periodic point growth in entropy rank one", Proc. Amer. Math. Soc., 136, 359-365 (2008). (Abstract, arXiv:math/0609510v1, bibtex, DOI, GS, MR2009g:37005, Zbl.1128.22004)

[48] R. Miles & T. Ward; "Periodic point data detects subdynamics in entropy rank one" Ergodic Theory and Dynamical Systems, 26, No. 6, 1913-1930 (2006) (Abstract, arXiv:math/0602665v1, bibtex, DOI, GS, Zbl.1142.37012)

[47] G. Everest, R. Miles, S. Stevens & T. Ward; "Orbit-counting in non-hyperbolic dynamical systems" Journal für die reine und angewandte Mathematik (Crelle's journal), 608, 155-182, 2007. (Abstract, arXiv:math/0511569v1, bibtex, DOI, GS, MR2008k:37042, Zbl.1137.37006)

[46] R. Miles & T. Ward; "Mixing actions of the rationals" Ergodic Theory and Dynamical Systems, 26, No. 6, 1905-1911 (2006) (Abstract, arXiv:math/0501142v1, bibtex, DOI, GS, MR2008c:37013, Zbl.1119.37005)

[45] G. Everest, S. Stevens, D. Tamsett & T. Ward; "Primes generated by recurrence sequences" Amer. Math. Monthly, 114, 417-431 (2007). (abstract, arXiv:math/0412079v2, bibtex, GS, MR2008b:11019)

[44] T. Ward; "Mixing and tight polyhedra" in Dynamics & Stochastics: Festschrift in Honor of M. S. Keane (Dee Denteneer, Frank den Hollander and Evgeny Verbitskiy, Editors) IMS Lecture Notes - Monograph Series, 48, 168-174, 2006. (Abstract, bibtex, DOI, GS, MR2008d:22007, Zbl.1167.37304).

[43] G. Everest, G. Mclaren & T. Ward; "Primitive divisors of elliptic divisibility sequences" Journal of Number Theory 118 No. 1, 71-89, 2006 (Abstract, arXiv:math/0409540v2, bibtex, DOI, GS, MR2007a:11074, Zbl.1093.11038)

[42] G. Everest, V. Stangoe & T. Ward; "Orbit counting with an isometric direction" Contemporary Mathematics, 385, 293-302, 2005. (Abstract, arXiv:math/0407166v1, bibtex, GS, MR2006k:37046, Zbl.1115.37015)

[41] M. Einsiedler & T. Ward; "Isomorphism rigidity in entropy rank two" Israel Journal of Mathematics, 147, 269-284, 2005. (Abstract, arXiv:math/0309161v1, bibtex, DOI, GS, MR2006m:28022)

[40] M. Einsiedler & T. Ward; "Entropy geometry and disjointness for zero-dimensional algebraic actions" Journal für die reine und angewandte Mathematik (Crelle's journal), 584, 195-214, 2005. (Abstract, arXiv:math/0211447v1, bibtex, DOI, GS, MR2006g:37004)

[39] S. Bhattacharya & T. Ward; "Finite entropy characterizes topological rigidity" Ergodic Theory and Dynamical Systems, 25, 365-373, 2005. (Abstract, arXiv:math/0302039v1, bibtex, DOI, GS, MR2006g:37003 , Zbl.1076.37004)

[38] T. Ward; "Group automorphisms with few and with many periodic points" Proc. Amer. Math. Soc., 133, 91-96, 2005. (Abstract, arXiv:math/0306292v1, bibtex, DOI, GS, MR2005f:37054 , Zbl.1052.37017)

[37] M. Einsiedler, G. Everest & T. Ward; "Periodic points for good reduction maps on curves", Geometriae Dedicata, 106, 29-41, 2004. (Abstract, arXiv:math/0307089v1, bibtex, DOI, GS, MR2005e:11085 , Zbl.1048.11091)

[36] Graham Everest, Alf van der Poorten, Yash Puri & Thomas Ward; "Integer sequences and periodic points", Journal of Integer Sequences, 5:Article 02.2.3, 2002. (Abstract, bibTeX, GS, MR2003j:11014 , Preprint in pdf, Related web site, Zbl.1026.11022)

[35] G. Everest, P. Rogers & T. Ward; "A higher-rank Mersenne problem", ANTS V Proceedings, Springer Lecture Notes in Computer Science, 2369, 95-107, 2002. (Abstract, bibTeX, GS, OpenURL, Preprint in pdf (© Springer-Verlag), MR2005d:11179 , Zbl.1071.11072)

[34] M. Einsiedler & T. Ward; "Asymptotic geometry of non-mixing sequences", Ergodic Theory and Dynamical Systems, 23(1), 75-85 (2003). (Abstract, arXiv:math/0204174v1, bibTeX, DOI, GS, MR2004c:37032 , Zbl.1039.37001 )

[33] Graham Everest & Thomas Ward; "Primes in divisibility sequences", Cubo Matemática Educacional, 3, No. 2, 245-259, 2001. (Abstract, bibTeX, GS, MR2003m:11043 , Preprint in pdf, Zbl.1082.11004)

[32] Yash Puri & Thomas Ward; "Arithmetic and growth of periodic orbits", Journal of Integer Sequences, 4:Article 01.2.1, 2001. (Abstract, arXiv:math/9907003v2, bibTeX, GS, MR2002i:11026 , Related web site, Zbl.1004.11013)

[31] M. Einsiedler, G. Everest & T. Ward; "Primes in elliptic divisibility sequences", LMS Journal of Computation and Mathematics, 4, 2001, 1-13. (Abstract, bibTeX, full text from LMS, GS, MR2002e:11181 , Zbl.1037.11089)

[30] M. Einsiedler, G. Everest & T. Ward; "Entropy and the canonical height", Journal of Number Theory, 91, No. 2 (2001), 256-273. (Abstract, bibTeX, DOI, GS, MR2003f:11092 , Zbl.0994.11022)

[29] G. Everest & T. Ward; "The canonical height of an algebraic point on an elliptic curve", New York Journal of Mathematics, 6 (2000), 331-342. (Abstract, bibTeX, full text from NYJM, GS, MR2001j:11056 , preprint in pdf, Zbl.0973.11062)

[28] M. Einsiedler, G. Everest & T. Ward; "Morphic heights and periodic points", New York Number Theory Seminar 2003, D. Chudnovsky, G. Chudnovsky, M. Nathanson (eds). Springer-Verlag 2004, ISBN: 0-387-40655-7. (Abstract, bibTeX, GS, MR2004m:11102 , Preprint in pdf, Zbl.1048.11091)

[27] T. Ward; "Additive cellular automata and volume growth", Entropy, 2, 142-167, 2000. (Abstract, bibTeX, DOI, GS, MR2004h:37014 , Preprint in pdf, Zbl.0999.68130)

[26] Y. Puri & T. Ward; "A dynamical property unique to the Lucas sequence", Fibonnaci Quarterly, 39.5, November 2001, 398-402. (arXiv:math/9907015v1, bibTeX, GS, MR2002j:37020, full text, related web site, Zbl.1018.37009)

[25] M. Einsiedler, G. Everest & T. Ward; "Primes in sequences associated to polynomials (after Lehmer)", LMS Journal of Computation and Mathematics, 3, 2000, 125-139. (Abstract, bibTeX, full text from LMS, GS, MR2002a:11017 , Preprint in pdf, Zbl.1037.11014)

[24] M. Einsiedler, D. Lind, R. Miles & T. Ward; "Expansive subdynamics for algebraic Z^d-actions", Ergodic Theory and Dynamical Systems, 21 (2001), no. 6, 1695-1729. (Abstract, arXiv:math/0104261v1, bibTeX, DOI, full text from CUP, GS, MR2004c:37033, preprint at Erwin Schrödinger Institute, Zbl.1003.37003)

[23] M. Einsiedler & T. Ward; "Fitting ideals for finitely presented algebraic dynamical systems", Aequationes Mathematicae, 60, No. 1-2, 2000, 57-71. (Abstract, arXiv:math/9907010v1, bibTeX, DOI, GS, MR2001j:22007, preprint at Erwin Schrödinger Institute, Zbl.0972.22005)

[22] P. D'Ambros, G. Everest, R. Miles & T. Ward: "Dynamical systems arising from elliptic curves", Colloquium Mathematicum 84-85, No. 1, 2000, 95-107. (Abstract, arXiv:math/9907014v1, bibTeX, GS, MR2001m:11093, Zbl.0965.37020)

[21] T. Ward: "Dynamical zeta functions for typical extensions of full shifts", Finite Fields and their Applications 5, No.3, 1999, 232-239. (Abstract, arXiv:math/9905175v1, bibTeX, DOI, GS, MR2000m:11067, Zbl.956.37016)

[20] G. Everest & T.Ward: "A dynamical interpretation of the global canonical height on an elliptic curve", Experimental Mathematics 7:4, 1998, 315-326. (Abstract, bibTeX, Full text from Exp. Math., GS, MR2000f:11079, Zbl.927.11009)

[19] G. Morris & T.Ward: "Entropy bounds for endomorphisms commuting with K actions", Israel Journal of Mathematics 106, 1998, 1-12. (Abstract, bibTeX, DOI, GS, MR99m:28042, Preprint in pdf, Zbl.931.22004)

[18] T. Ward; "A family of Markov shifts (almost) classified by periodic points" Journal of Number Theory 71, 1998, 1-11. (Abstract, bibTeX, DOI, GS, MR99j:11089, Zbl.935.28008)

[17] T. Ward: "Almost all S-integer dynamical systems have many periodic points", Ergodic Theory and Dynamical Systems 18, 1998, 471-486. (Abstract, bibTeX, DOI, GS, preprint at Erwin Schrödinger Institute, MR99k:58152, Zbl.915.58081)

[16] G. Morris & T. Ward: "A note on mixing properties of invertible extensions", Acta Math. Univ. Comenianae 66, No.2, 1997, 307-311. (Abstract, bibTeX, Full text from AMUC, GS, MR99j:28018, Zbl.924.28014)

[15] T. Ward: "Three results on mixing shapes", New York Journal of Mathematics 3A, 1997, 1-10. (Abstract, bibTeX, Full text from NYJM, GS, MR99e:28031, Preprint in pdf, Zbl.909.28015)

[14] T. Ward: "An uncountable family of group automorphisms, and a typical member", Bulletin London Mathematical Society 29, 1997, 577-584. (Abstract, bibTeX, DOI, GS, MR98k:22028, Preprint in pdf, Zbl.903.22001)

[13] V. Chothi, G. Everest & T. Ward: "S-integer dynamical systems: periodic points", Journal für die reine und angewandte Mathematik (Crelle's journal) 489, 1997, 99-132. (Abstract, bibTeX, DOI, GS, MR99b:11089, Preprint in pdf, Zbl.879.58037)

[12] T. Ward: "Rescaling of Markov shifts", Acta Math. Univ. Comenianae 65, No.1, 1996, 149-157. (Abstract, bibTeX, Full text from AMUC, GS, MR98d:58053, Preprint in pdf, Zbl.866.22006)

[11] V. Chothi, G. Everest & T. Ward: "Oriented local entropies for expansive actions by commuting automorphisms", Israel Journal of Mathematics 93, 1996, 281-301. (Abstract, bibTeX, DOI, GS, MR97i:28012, Preprint in pdf (text only), Zbl.848.22013)

[10] T. Ward: "Additive relations in fields: an entropy approach", Journal of Number Theory 53, 1995, 137-143. (Abstract, bibTeX, DOI, GS, MR97d:11126, Zbl.841.11035)

[9] T. Ward: "Automorphisms of Z^d-subshifts of finite type", Indagationes Mathematicae 5(4), 1994, 495-504. (Abstract, bibTeX, DOI, GS, MR97a:28014, Preprint in pdf, Zbl.823.28007)

[8] K. Schmidt & T. Ward: "Mixing automorphisms of compact groups and a theorem of Schlickewei", Inventiones Mathematicae 111, 1993, 69-76. (Abstract, bibTeX, DOI, EMANI, GS, MR95c:22011, Preprint in pdf, Zbl.824.28012)

[7] T. Ward: "An algebraic obstruction to isomorphism of Markov shifts with group alphabets", Bulletin London Mathematical Society 25, 1993, 240-246. (Abstract, bibTeX, DOI, GS, MR94g:22013, Preprint in pdf, Zbl.792.22004)

[6] T. Ward & Q. Zhang: "The Abramov-Rokhlin entropy addition formula for amenable group actions", Monatshefte für Mathematik 114, 1992, 317--329. (Abstract, bibTeX, DOI, EMANI, GS, MR93m:28023, Zbl.764.28014)

[5] T. Ward: "The Bernoulli property for expansive Z² actions on compact groups", Israel Journal of Mathematics 79, 1992, 225-249. (Abstract, bibTeX, DOI, GS, MR94k:28031, Preprint in pdf, wordle, Zbl.789.28014)

[4] T. Ward: "Periodic points for expansive actions of Z^d on compact abelian groups", Bulletin London Mathematical Society 24, 1992, 317-324. (Abstract, bibTeX, DOI, GS, MR93h:22010, Preprint in pdf, wordle, Zbl.760.22005)

[3] T. Ward: "Almost block independence for the three dot Z² dynamical system", Israel Journal of Mathematics 76, 1991, 237-256. (Abstract, bibTeX, DOI, GS, MR93h:28032, Preprint in pdf, wordle, Zbl.790.28013)

[2] D.A. Lind, K. Schmidt & T. Ward: "Mahler measure and entropy for commuting automorphisms of compact groups", Inventiones mathematicae 101, 1990, 593-629. (Abstract, bibTeX, DOI, EMANI, full text, GS, MR92j:22013, wordle, Zbl.774.22002)

[1] D.A. Lind & T. Ward: "Automorphisms of solenoids and p-adic entropy", Ergodic Theory and Dynamical Systems 8, 1988, 411-419. (Abstract, bibTeX, DOI, full text, GS, MR90a:28031, wordle, Zbl.634.22005)

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Books

[5] "Entropy in dynamics, Manfred Einsiedler, Elon Lindenstrauss & Thomas Ward. In preparation; 8 chapters available in draft form.

[4] "Ergodic Theory with a view towards Number Theory", Manfred Einsiedler & Thomas Ward. Springer Graduate Texts in Mathematics (GTM), Vol. 259. 1st Edition., October 2010, 467 p. 52 illus. ISBN: 978-0-85729-020-5. (bibTeX, GS, Zbl.1206.37001)

[3] "An Introduction to Number Theory", Graham Everest & Thomas Ward. Springer Graduate Texts in Mathematics (GTM), Vol. 232; 1st ed. 2005. X, 302 p., 16 illus., Hardcover ISBN: 978-1-85233-917-3. (bibTeX, MR2006j:11001, Zbl.1089.11001, GS)

• Corr. 2nd printing, 2006
• Reprint 丛书名: 国外数学名著系列(影印版) = Foreign Math Classic series (copy version), Science Press, Beijing, 2011. ISBN 9787030313867

[2] "Recurrence sequences", Graham Everest, Alf van der Poorten, Igor Shparlinski & Thomas Ward. Amer. Math. Society Surveys and Monographs, 104 2003; 318 pp., ISBN 0-8218-3387-1. (Supplementary material at the AMS, bibTeX, MR2004c:11015, Zbl.1033.11006, GS)

[1] "Heights of Polynomials and Entropy in Algebraic Dynamics", Graham Everest and Thomas Ward. Springer Verlag. 1999; XII, 212 pp. 23 figs. ISBN 1-85233-125-9, (bibTeX, MR2000e:11087 , Zbl.919.11064, Preface, GS)

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Edited proceedings

[1] "Algebraic and Topological Dynamics", Sergiy Kolyada, Yuri Manin & Thomas Ward (eds). Contemporary Mathematics, Amer. Math. Society, Volume 385 (2005). (MR2006e:37002 , Zbl.1075.37001)

[2] "Dynamical Numbers: Interplay between Dynamical Systems and Number Theory", Sergiy Kolyada, Yuri Manin, Martin Möller, Pieter Moree & Thomas Ward (eds). Contemporary Mathematics, Amer. Math. Society, Volume 532 (2010).

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Surveys and Essays

[3] T. Ward; A response to the article "Putting reality back into the equation", Times Higher Education Supplement, 20 Jan. 2011

[2] T. Ward: "Ergodic theory: interactions with combinatorics and number theory" to appear in Encyclopedia of Complexity and Systems Science, Part 5, 3040-3053, Springer Verlag (2009). (DOI, pdf file, GS)

[1] T. Ward: "Ergodentheorie: von Planetenbahnen zur Zahlentheorie", Max-Planck Institute für Mathematik Jahrbuch, 2005. (Preprint in pdf)

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Book reviews

[20] "Dynamical systems: Stability, controllability and chaotic behaviour", by Werner Krabs and Stefan Pickl, Springer Berlin (2010).

[19] "A nonlinear dynamics perspective of Wolfram's new kind of science", Vol. 3, by Leon O. Chua, World Scientific Series on Nonlinear Science. Series A 68. Hackensack, NJ: World Scientific (2009). Zentralblatt 1185.37017.

[18] "Smooth ergodic theory for endomorphisms", by Min Qian, Jian-Sheng Xie and Shu Zhu, Springer Lecture Notes in Mathematics, Vol. 1978. (2009). Zentralblatt 1182.37003.

[17] "A nonlinear dynamics perspective of Wolfram's new kind of science", Vol. 2, by Leon O. Chua, World Scientific Series on Nonlinear Science. Series A 57. Hackensack, NJ: World Scientific (2007). Zentralblatt 1135.37001.

[16] "The arithmetic of dynamical systems" by Joseph Silverman, Graduate Texts in Mathematics, 241. Springer, New York, 2007. Math. Reviews MR2316407 and Zentralblatt

[15] "p-adic deterministic and random dynamical systems" by Andrei Khrennikov and Marcus Nilsson, Mathematics and its Applications Vol. 574, Kluwer Academic Publishers (2004). Bulletin American Math. Society 43 (2006), 133-137.

[14] "Multidimensional continued fractions" by Fritz Schweiger, Oxford University Press (2000). Math. Reviews MR2005i:11090

[13] "Computational ergodic theory" by Geon Ho Choe, Springer-Verlag (2005). Zentralblatt 1064.37004.

[12] "Topics in orbit equivalence" by Alexander S. Kechris and Benjamin D. Miller, Lecture Notes in Mathematics Vol. 1852. Springer (2004). Zentralblatt 1058.37003.

[11] "Ergodic theory of numbers" by Karma Dajani and Cor Kraaikamp, Carus Mathematical Monographs, 29. Mathematical Association of America, Washington, DC, 2002. Math. Reviews MR2003f:37014.

[10] Review of Word2TeX and TeX2Word (Chikri Software), MSOR Connections Nov. 2003, Vol. 3 No. 4.

[9] "Restricted orbit equivalence for actions of discrete amenable groups" by Janet Whalen Kammeyer and Daniel J. Rudolph, Cambridge Tracts in Mathematics, 146. Cambridge University Press, Cambridge, 2002. Zentralblatt 0992.43001.

[8] "Experimental Mathematics with MAPLE" by Franco Vivaldi, Chapman and Hall/CRC (2001). Zentralblatt 0962.00001.

[7] "Single Orbit Dynamics" by Benjamin Weiss, CBMS Regional Conference Series in Mathematics, 95. American Math. Society, Providence, RI, 2000. Math. Reviews MR2000k:37001.

[6] "Metric Diophantine Approximation on Manifolds" by V.I. Bernik and M.M. Dodson, Cambridge University Press (1999). Zentralblatt 933.11040.

[5] "Basic Ergodic Theory" by M.G. Nadkarni, Birkhaüser (1998). Zentralblatt 908.28014.

[4] "From Calculus to Chaos" by D. Acheson, Oxford University Press (1997). Math. & Stats. 9:4, 1998.

[3] "Ergodic Theory of Fibred Systems and Metric Number Theory" by F. Schweiger, Oxford Science Publications (1995). Math. Reviews MR97h:11083

[2] "Dynamical Systems of Algebraic Origin" by K. Schmidt, Birkhaüser (1995). Bulletin London Mathematical Society 29, 1997, 502-504.

[1] "Ergodic Theory of Z^d-actions", M. Pollicott and K. Schmidt (eds). Proceedings of the Warwick Symposium 1993-94. LMS Lecture Notes 228, Cambridge University Press. Ergodic Theory and Dynamical Systems 16, 1996, 1105-1108. (DOI)

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