- [98] Paul Glendinning (2018) Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations, European Journal of Applied Mathematics, 29(5), 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
**7**27-37 - [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)

- [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

- 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.

Back to my home page