Preprints, papers and books

Preprints

Publications: articles and books

• [114] Paul Glendinning and David J.W. Simpson (2023) Differentiable conjugacies for one-dimensional maps, to appear “Advances in Discrete Dynamical Systems, Difference Equations, and Applications” eds. S. Olaru, S. Elaydi, J. Cushing and R. Lozi, Springer Proceedings in Mathematics & Statistics series. https://arxiv.org/abs/2303.00115
• [113] Paul Glendinning, S. John Hogan, Martin Homer, Mike R. Jeffrey and Robert Szalai (2023) Uncountably many cases of Filippov's sewed focus, to appear Jornal of Nonlinear Science.
• [112] P.A. Glendinning and D.J.W. Simpson (2023) Normal Forms, Differentiable Conjugacies and Elementary Bifurcations of Maps, SIAM Journal on Applied Mathematics, 83, 816-836. doi.org/10.1137/22M1503701, arXiv 2206.04840
• [111] P.A. Glendinning and D.J.W. Simpson (2022) Normal Forms for Saddle-Node Bifurcations: Takens' Coefficient and Applications in Climate Models, Proc. R. Soc. A. 478 20220548. doi.org/10.1098/rspa.2022.0548, arXiv 2208.09633.
• [110] P.A. Glendinning and D.J.W. Simpson (2022) Chaos in the Border-Collision Normal Form: A Computer-Assisted Proof Using Induced Maps and Invariant Expanding Cones, Appl. Math. Comput. 434, 127357, doi.org/10.1016/j.amc.2022.127357.
• [109] Joshua Hawley, Cerys Manning, Veronica Biga, Paul Glendinning and Nancy Papalopulu (2022) Dynamic switching of lateral inhibition spatial patterns, J. Roy. Soc. Interface, doi.org/10.1098/rsif.2022.0339.
• [108] Paul Glendinning and Sasha Glendinning Smooth conjugacy of difference equations derived from elliptic curves. (2021) J. Diff. Equ. Appl. doi.org/10.1080/10236198.2021.1984441
• [107] Gianne Derks, Paul A. Glendinning, Anne C. Skeldon (2021) Creation of discontinuities in circle maps, Proc. Roy. Soc. A, 477, 20200872
• [106] Biga V, Hawley J, Soto, X, Johns E, Han D, Bennett H, Adamson A.D, Kursawe, J, Glendinning P, Manning C. and Papalopulu N. A dynamic, spatially periodic, micro-pattern of HES5 underlies neurogenesis in the mouse spinal cord (2021), to appear Molecular Systems Biology.
• [105] P. Glendinning and M.R. Jeffrey (2021) Hidden dynamics for piecewise smooth maps, Nonlinearity, 34, 3184. https://doi.org/10.1088/1361-6544/abe734.
• [104] Paul A. Glendinning and David J.W. Simpson (2021) A constructive approach to robust chaos using invariant manifolds and expanding cones, Disc. Cont. Dynam. Syst. Series A, Discrete & Continuous Dynamical Systems - A (DCDS-A) 41(7) doi:10.3934/dcds.2020409.
• [103] RN Thompson, TD Hollingsworth, V Isham, D Arribas-Bel, B Ashby, and many others including P. Glendinning (2020) Key questions for modelling COVID-19 exit strategies, Proc. Roy. Soc. B 287 20201405.
• [102] Paul A. Glendinning and David J.W. Simpson (2020) Robust Chaos and the Continuity of Attractors, Trans. Math. & Its Appl. 4(1) doi.org/10.1093/imatrm/tnaa002.
• [101] Paul Glendinning (2020) Adaptive resonance and pumping a swing. European Journal of Physics, 41 025006, doi.org/10.1088/1361-6404/ab6a63.
• [100] Paul Glendinning and Mike R. Jeffrey (2019) An Introduction to Piecewise Smooth Dynamics, Birkh\"auser.
• [99] S. Webber, P. Glendinning and M.R. Jeffrey (2019) Pausing for arbitrarily long times in dynamical systems Proc. Roy. Soc. A 475, 2221, 20180574.
• [98] Paul Glendinning (2018) Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations EJAM 29, 757--777.
• [97] Paul Glendinning (2018) Three haiku J. Humanistic Math. 8(1), 454.
• [96] Paul Glendinning (2017) Less Is More II: An Optimistic View of Piecewise Smooth Bifurcation Theory, pp. 77-81 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
• [95] Paul Glendinning (2017) Less Is More I: A Pessimistic View of Piecewise Smooth Bifurcation Theory, pp. 71-75 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
• [94] Chris Budd, Paul Glendinning, Kaitlin Hill, and Rachel Kuske (2017) Characterizing Tipping in a Stochastic Reduced Stommel-Type Model in Higher-Dimensions, pp. 25-29 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
• [93] E. Bossolini, R. Edwards, P. A. Glendinning, M. R. Jeffrey, S. Webber (2017) Regularization by External Variables, pp. 19-24 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
• [92] Paul Glendinning (2017) Robust chaos revisited, European Physical Journal Special Topics, 226: 1721. doi:10.1140/epjst/e2017-70058-2
• [91] Paul Glendinning (2016) Geometry of refractions and reflections through a biperiodic medium, SIAM J. Appl. Math., 76(4), 1219–1238
• [90] Paul Glendinning, Piotr Kowalczyk and Arne Nordmark (2016) Multiple attractors in grazing-sliding bifurcations in an explicit example of Filippov type, IMA J Appl Math. doi: 10.1093/imamat/hxw014.
• [89] Paul Glendinning (2016) Bifurcation from stable fixed point to two-dimensional attractor in the border collision normal form, IMA J. Appl. Math. doi: 10.1093/imamat/hxw001
• [88] Paul Glendinning (2016) Classification of Boundary Equilibrium Bifurcations of planar Filippov systems, Chaos 26, 013108; http://dx.doi.org/10.1063/1.4940017
• [87] Paul Glendinning (2015) Bifurcation from stable fixed point to $N$-dimensional attractor in the border collision normal form, Nonlinearity 28(10): 3457-3464.
• [86] N. J. Higham (Editor) Princeton Companion to Applied Mathematics, Princeton, 2015 (Associate Editor and Contributor).
• [85] P. Glendinning and N. Sidorov (2015) The doubling map with asymmetric holes, Ergod. Th.& Dynam. Syst. 35, 1208 - 1228 DOI:10.1017/etds.2013.98 [21 pages]
• [84] P Glendinning and M R Jeffrey (2015) Grazing-sliding bifurcations, border collision maps and the curse of dimensionality for piecewise smooth bifurcation theory, Nonlinearity 28 263-283 (doi:10.1088/0951-7715/28/1/263) -- very early draft on eprints.
• [83] Andrew Roberts and Paul Gendinning (2014) Canard-like phenomena in piecewise-smooth Van der Pol systems, Chaos 24, 02313; http://dx.doi.org/10.1063/1.4885502
• [82] P. Glendinning (2014) Invariant Measures for the n-Dimensional Border Collision Normal Form, IJBC 24 (12) 1450164 DOI: 10.1142/S0218127414501648
• [81] P.Glendinning (2014) Renormalization for the boundary of chaos in piecewise monotonic maps with a single discontinuity, Nonlinearity 27 R143-R162 (doi:10.1088/0951-7715/27/12/R143)
• [80] V. Botella-Soler and P.Glendinning (2014) Hierarchy and polysynchrony in an adaptive network. Phys. Rev. E 89 062809.
• [79] Mora, Karin; Budd, Chris; Glendinning, Paul; Keogh, Patrick (2014) Non-smooth Hopf-type bifurcations arising impact–friction contact events in rotating machinery. Proc. Roy. Soc. A, 470: 20140490.
• [78] Paul Glendinning (2014) The Border Collision Normal Form with Stochastic Switching Surface. SIAM J. Applied Dynamical Systems 13, 181-193
• [77] P. Kowalczyk, S. Nema, P. Glendinning, I. Loram, and M. Brown (2014) "Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing." Chaos: An Interdisciplinary Journal of Nonlinear Science 24: 022101.
• [76] 50 Visions of Mathematics (2014) Ed. Sam Parc [PG is the ‘P’], OUP.
• [75] M. Goodfellow and P. Glendinning (2013) Mechanisms of Intermittent State Transitions in a Coupled Heterogeneous Oscillator Model of Epilepsy, J. Math. Neuroscience, 3, 17 doi:10.1186/2190-8567-3-17
• [74] V. Botella-Soler, J.A. Oteo, J. Ros and P. Glendinning (2013) Lyapunov exponent and topological entropy plateaus in piecewise linear maps J. Phys. A: 46, 125101 [26 pages]
• [73] P. Glendinning and L.A. Smith (2013) Lacunarity and period-doubling, Dyn. Syst. IJ, DOI:10.1080/14689376.2012.755496 [11 pages]
• [72] P. Glendinning, P. Kowalczyk and A.B. Nordmark (2012) Attractors near grazing-sliding bifurcations, Nonlinearity 25 1867--1885.
• [71] P. Glendinning (2012) Maths In Minutes, Quercus. [410 small pages]
• [70] V. Botella-Soler and P. Glendinning (2012) Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems, EPL, 97, 50004.
• [69] M. Pailha, A. L. Hazel, P. A. Glendinning, and A. Juel (2012) Oscillatory bubbles induced by geometrical constraint, Physics of Fluids, 24, 021702-1-021702-7
• [68] P. Kowalczyk, P. Glendinning, M. Brown, G. Medrano-Cerda, H. Dallali, J. Shapiro (2012) Modelling human balance using switched systems with linear feedback control, J Roy Soc Interfac, 9, 234-245.
• [67] P. Glendinning (2011) Two Ball Newton Cradle, Phys. Rev. E, 84:067201
• [66] K. Liao, R.M. Schneider, S.S. Yaniglos, G. Bertolini, P. Glendinning, R.N. Sawyer, Jr., M. Reschke, and R.J. Leigh (2011) Visual and vestibular determinants of the translational vestibulo-ocular reflex, Ann. NY Acad. Sci., 1233, 263-270.
• [65] P. Glendinning and P. Kowalczyk (2011) ‘Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems.’ Chaos. 21:023126 [11 pages].
• [64] R. Vitolo, P. Glendinning and J. Gallas (2011) ‘Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative’, Phys. Rev. E 84, 016216 [7 pages]
• [63] P. Glendinning and C.H. Wong (2011) Two-dimensional attractors in the border-collision normal form, Nonlinearity, 24, 995-1010.
• [62] P. Glendinning (2010) Bifurcations of snap-back repellers with application to the border-collision normal form', Int. J. Bifn. Chaos 20, 479-489
• [61] P. Glendinning and P. Kowalczyk (2010) 'Micro-chaotic dynamics due to digital sampling in hybrid systems of Filippov type', Physica D, 239, 58-71
• [60] P. Glendinning and P. Kowalczyk (2009) 'Dynamics of a hybrid thermostat model with discrete sampling time control', Dynamical Systems IJ, 23 343-360.
• [59] P. Glendinning, T. Jaeger and J. Stark (2009) `Strangely dispersed minimal sets in the quasiperiodically forced Arnold circle map', Nonlinearity 22 835-854
• [58] 'Border collision bifurcations, snap-back repellers, and chaos' (2009) Physical Review E (Vol.79, No.2): DOI: 10.1103/PhysRevE.79.025202 (with C.H. Wong).
• [57] ‘How chaotic are strange non-chaotic attractors?’ (2006) Nonlinearity, 19, 2005-2023 (with G.Keller and T.Jaeger).
• [56] 'Routes to Chaos' (2005) Encyclopedia of Nonlinear Science Ed A. Scott, Routledge, New York pp. 814-817.
• [55] 'Invariant manifolds and sets' (2005) Encyclopedia of Nonlinear Science Ed A. Scott, Routledge, New York pp. 465-467.
• [54] 'Henon map' (2005) Encyclopedia of Nonlinear Science Ed A. Scott, Routledge, New York pp. 403-406.
• [53] `The non-smooth pitchfork bifurcation' (2004) Discrete and Continuous Dynamical Systems B 4, 457-464 (pdf file, 1.5M)
• [52] `The mathematics of motion camouflage' (2004) Proc. Roy. Soc. (London) Series B 271 477-481 available as a pdf file.
• [51] `The accumulation of boundary doubling for modified tent maps' (2003) Trends in Mathematics: Bifurcations, Symmetry and Patterns Eds. J. Buescu, S.B.S.D. Castro, A.P.S. Dias \& I.S. Labouriau, Birkhauser, Basel. This note is available as a dvi file.
• [50] `Stability of asymmetric cluster states in globally coupled maps' (2003) Proceedings of the 2003 Workshop on Nonlinear Dynamics of Electronic Systems ed. R. Stoop, 89-92, Universitat Zurich. This paper is available as a pdf file
• [49] `Global attractors of pinched skew products' (2002) Dyn. Syst. IJ 17 287-297. This paper is available as a dvi file.
• [48] `Rotation numbers for quasi-periodically forced monotone circle maps' (2002) Dyn. Sys. IJ 17 1-28 (with J. Stark, U. Feudel and A.S. Pikovsky). A pdf version of this paper can be downloaded here.
• [47] `Imperfect Homoclinic Bifurcations' (2001) Phys. Rev. E 64 036208 (8 pages) (with J. Abshagen and T. Mullin)
• [46] `Multistability in the quasiperiodically forced circle map' (2001) IJBC 11 3085-3105 (with H. Osinga, U. Feudel and J. Wiersig). This paper has its very own web site which has loads of pretty pictures (in colour) and explanatory text.
• [45] `Unique representations of real numbers in non-integer bases' (2001) Math. Res. Lett. 8 535-543 (with N. Sidorov). A dvi file is available.
• [44] `Hyperbolicity of the invariant set for the logistic map with mu > 4' (2001) Nonlinear Analysis: Theory, Methods & Applications 47 3323-3332. This note is basically pedagogical, but contains a new and very simple proof of the result. It can be downloaded as a dvi file.
• [43] From finite to infinite dimensional dynamical systems (2001) Editor, with J.C. Robinson, and co-author of Introduction. Kluwer NATO Science Series, II. Math., Phys.and Chem. 19, 215 pages.
• [42] `Milnor attractors and topological attractors in a piecewise linear map' (2001) Nonlinearity 14 239-258. Available as a dvi file.
• [41] `The structure of mode-locked regions in quasi-periodically forced circle maps' (2000) Physica D 140 227-243 (with U. Feudel, A.S. Pikovsky and J. Stark). This paper is available in ps format.
• [40] `Transitivity and blowout bifurcations in a class of globally coupled maps' (1999) Phys. Lett. A 264 303-310 (pdf -- text only)
• [39] `The stability boundary of synchronized states in globally coupled dynamical systems' (1999) Phys. Lett. A 259 129-134
• [38] `Fine structure of mode-locked regions of the quasi-periodically forced circle map' (1999) Phys. Lett. A 257 65-69 (with J. Wiersig)
• [37] `Towards a quasi-periodic mean field theory of globally coupled oscillators' (1999) Phys. Lett. A 251 297-302 (with M. Banaji)
• [36] `Intermittency and strange nonchaotic attractors in quasi-periodically forced circle maps' (1998) Phys. Lett. A 244 545-550
• [35] `Melnikov analysis of chaos in a simple epidemiological model' (1997) J. Math. Biol. 35 359-373 (with L.P. Perry)
• [34] `Bifocal homoclinic bifurcations' (1997) Physica D 102 1-14 (with C.R. Laing)
• [33] `Inaccessible attractors of weakly dissipative systems' (1997) Nonlin. 10 507-522
• [32] `Differential equations with bifocal homoclinic orbits' (1997) Intl. J. Bifn. & Chaos 727-37
• [31] `Shilnikov's saddle-node bifurcation' (1996) Intl. J. Bifn. & Chaos 6 1153-1160 (with C. Sparrow)
• [30] `Zeros of the kneading invariant and topological entropy for Lorenz maps' (1996) Nonlin. 9 999-1014 (with T. Hall)
• [29] `A homoclinic hierarchy' (1996) Phys. Lett. A 211 155-160 (with C.R. Laing)
• [28] `Bifurcations and rotation numbers for maps of the circle associated with flows on the torus and models of cardiac arrythmias' (1995) Dyn. Stab. Sys. 10 367-386
• [27] `Locating bifurcations in quasiperiodically forced systems' (1995) Phys. Lett. A 200 17-26 (with P.R. Chastell and J. Stark)
• [26] Stability, Instability and Chaos: an introduction to the theory of nonlinear differential equations (1994) 388 pages, CUP
• [25] `Island chain models and gradient systems' (1994) J. Math. Biol. 32 171-178
• [24] `Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps' (1993) Physica D 62, 22-50 (with C. Sparrow)
• [23] `Travelling waves with spatially resonant forcing: bifurcations of a modified Landau equation' (1993) Int. J. Bifn. & Chaos 3, 1447-1455 (with M.R.E. Proctor)
• [22] `The anharmonic route to chaos: kneading theory' (1993) Nonlin. 6 349-367
• [21] `Robust new routes to chaos in differential equations' (1992) Phys. Lett. A 168 40-46
• [20] `Time series near codimension two global bifurcations' (1990) in Measures of complexity and chaos eds. N. Abraham, A. Albano, A. Passamante and P. Rapp, Plenum
• [19] `Renormalisation between classes of maps' (1990) Phys. Lett. A 145 109-112 (with J.E. Los and C. Tresser)
• [18] `Explicit renormalisation of some piecewise linear maps' (1990) Physica D 44 149-167 (with D. Veitch)
• [17] `Topological conjugation of Lorenz maps to $\beta$-transformations' (1990) Math. Proc. Camb. Phil. Soc. 107, 401-413
• [16] `Global structure of homoclinic bifurcations: a combinatorial approach' (1989) Phys. Lett. A 141 391-396
• [15] `Subsidiary bifurcations near bifocal homoclinic orbits' (1989) Math. Proc. Camb. Phil. Soc.105 597-605
• [14] `Dynamique symbolique pour la renormalisation des endomorphismes d'entropie nulle de l'intervalle' (1988) C. R. Acad. Sci. (Paris) S\'erie I 307 607-612 (with J.E. Los, M.V. Otero-Espinar and C. Tresser)
• [13] `The gluing bifurcation I: symbolic dynamics of the closed curves' (1988) Nonlinearity 1, 203-214 (with J.M. Gambaudo and C. Tresser)
• [12] `Global bifurcations in flows' (1988) in New directions in dynamical systems eds. T. Bedford and J. Swift, CUP
• [11] `Asymmetric perturbations of Lorenz-like equations' (1987) Dyn.Stab. Syst. 2, 1-11
• [10] `Travelling waves near isolated double-pulse solutions of nerveaxon equations', (1987) Phys. Lett. A 121, 411-413
• [9] `Homoclinic bifurcations in ordinary differential equations' (1987) in Chaos in biological systems, eds. H. Degn, A.V. Holden and L. Olson, Plenum, New York
• [8] `Stable cycles with complicated structures' (1987) in Instabilitiesand nonequilibrium structures, eds. E. Tirapegui and D. Villarroel, D.Reidel Publishing Co. (with J.M. Gambaudo and C. Tresser)
• [7] `T-points: a codimension two heteroclinic bifurcation' (1986) J. Stat. Phys. 43, 479-488 (with C. Sparrow)
• [6] `Stable cycles with complicated structures' (1985) J. Physique Lett. 46, L653-L658 (with J.M. Gambaudo and C. Tresser)
• [5] `Heteroclinic loops leading to hyperchaos' (1985) J. Physique Lett. 46, L347-L352 (with J.M. Gambaudo and C. Tresser)
• [4] `Collage de cycles et suites de Farey' (1984) C.R. Acad. Sci. S\'erie I, 300, 311-313 (with J.M. Gambaudo and C. Tresser)
• [3] `The rotation interval as a computable measure of chaos' (1984) Phys. Lett. A 105, 97-100 (with J.M. Gambaudo and C. Tresser)
• [2] `Bifurcations near homoclinic orbits with symmetry' (1984) Phys.Lett. A 103, 163-166
• [1] `Local and global behaviour near homoclinic orbits' (1984) J. Stat. Phys. 35, 645-696 (with C. Sparrow)

Lecture notes/theses/books in progress

• [1] `Homoclinic bifurcation' (1985) Ph.D. thesis, University of Cambridge
• [2] `Introduction to computational dynamics` (1988) lecture notes, 112 pages, for ICTP Summer School on Dynamical Systems, Trieste, 1988 (with J. Stark)
• [3] Chaos and routes to chaos in Lorenz maps (1992) an essay for the Adams Prize (223 pages), to become a book
• [4] Flow instability, chaos and turbulence (1993) lecture notes for industrial education programme at the Newton Institute (with H.K. Moffatt and M.R.E. Proctor)
• [5] Bifurcation Theory: codimension one bifurcations (1996) lecture notes for Nonlinear Mathematics School, Bristol
• [6] `Maps of the Circle' in One dimensional dynamics, (1996) TEMPUS Lecture Notes volume 14
• [7] Mathematical models in economics (1998) Queen Mary and Westfield College Lecture Notes, 115 pages, to become a book

Other writing

• Mathematics in the New Elizabethan Age (60 Years of British Mathematics) (with K. Brown) in Science in Parliament, 2012, reprinted in Mathematics Today, 2012.
• Mathematics Today (with K. Brown) in Science in Parliament, 2011, reprinted in Mathematics Today, 2011.
• `A physicist's tour of chaos' (review of Chaos in Dynamical Systems, E. Ott) 1994 Nature 368 26.
• `Translations: active and passive' in At one remove, ed. P. Curtis, 1998 (Henry Moore Institute)
• Ads that don't add up, The Guardian (Online section) 26 Nov. 1998.
• View from the Pennines: View from the Pennines Mathematics Today 48, 176—177, 2012
• View from the Pennines: An Odd Sympathy Mathematics Today 47, 240—241,2011
• View from the Pennines: Newton’s Cradle Mathematics Today 47, 190--191,2011
• View from the Pennines: Invisibility Mathematics Today 46,314—315, 2010.
• View from the Pennines: A Cosmic Indian Rope Trick Mathematics Today 46, 2010.
• View from the Pennines: Mind the (Generation) Gap Mathematics Today 46, 2010.
• View from the Pennines: Abstract Frost Fronts Mathematics Today 46, 39--40, 2010.
• View from the Pennines: Embed with causality Mathematics Today 45, 2009.
• View from the Pennines: Box Models of the Oceanic Conveyor Belt Mathematics Today 45, 2009.
• View from the Pennines: Beyond a Reasonable Doubt Mathematics Today 45, 119--120, 2009.
• View from the Pennines: Don't Panic Mathematics Today 45, 71--72, 2009.
• View from the Pennines: Falling leaves Mathematics Today 45, 30--32, 2009.
• View from the Pennines: Ballistic Penetration Mathematics Today 44, 253--254, 2008
• View from the Pennines: Beyond mal-rules Mathematics Today 44, 200--202, 2008.
• View from the Pennines: Accelerating Solitons Mathematics Today 44, 161--162, 2008.
• View from the Pennines: Strange Nonchaotic Attractors Mathematics Today 44, 119--120, 2008.
• View from the Pennines: Bossut and Viallet, and early example of industrial applied mathematics Mathematics Today 44, 77--79, 2008.
• View from the Pennines: Euler's Addition Formula Mathematics Today 43, 207--208, 2007.
• View from the Pennines: Euler goes ballistic Mathematics Today 43, 175--177, 2007.
• View from the Pennines: Euler's Gamma Function Mathematics Today 43, 137--139, 2007.
• View from the Pennines: Euler's Singularities Mathematics Today 43, 102--103, 2007.
• View from the Pennines: Euler gets kinky Mathematics Today 43, 65--66, 2007.
• View from the Pennines: Using Maths II, Tomography and Fritz John Mathematics Today 42, 168--169, 2006.
• View from the Pennines: Using Maths I, Tomography and Johann Radon Mathematics Today 42, 132--134, 2006.
• View from the Pennines: Carleson, Strange Attractors and the Abel Prize Mathematics Today 42, 99--101, 2006.
• View from the Pennines: A Glass of Bubbly Mathematics Today 42, 60--61, 2006.
• View from the Pennines: Montessori Mathematics Mathematics Today 42, 20--22, 2006.
• View from the Pennines: Seven plus or minus two Mathematics Today 41, 189--190, 2005.
• View from the Pennines: Ten Martinis and Fractal Carpets Mathematics Today 41, 151--152, 2005.
• View from the Pennines: Systems Biology Mathematics Today 41, 120--121, 2005.
• View from the Pennines: Hold on to your triangles Mathematics Today 41, 91--92, 2005.
• View from the Pennines: What the n-1? Mathematics Today 41, 61--63, 2005.
• View from the Pennines: The Poincar\'e Comjecture Mathematics Today 41, 28--29, 2005.
• View from the Pennines: Prefeerence and Utility Mathematics Today 40, 209--210, 2004.
• View from the Pennines: Making the best of a Poor Deal Mathematics Today 40, 174--175, 2004.
• View from the Pennines: Pole Decomposition Mathematics Today 40, 130--131, 2004.
• View from the Pennines: Bird's Nest Architecture Mathematics Today 40, 103--104, 2004.
• View from the Pennines: Pattern Complexity Mathematics Today 40 65--66, 2004.
• View from the Pennines: On art and causal sets Mathematics Today 40, 32--33, 2004.
• View from the Pennines: Sticky Waves Mathematics Today 39, 198--199, 2003.
• View from the Pennines: Analysis on Time Scales Mathematics Today 39, 156--159, 2003.
• View from the Pennines: Non-trivial Pursuits Mathematics Today 39, 118--120, 2003.
• View from the Pennines: Almost Automorphisms Mathematics Today 39, 85--86, 2003.
• View from the Pennines: Ideal Knots Mathematics Today 39, 60--61, 2003.
• View from the Pennines: Making connections Mathematics Today 39, 26--27, 2003.
• View from the Pennines: Newtonian choreographies Mathematics Today 38, 184--185, 2002.

To download some of the View from the Pennines articles go to the View from the Pennines homepage.