Preprints, papers and books
Paul Glendinning (2017) Robust Chaos Revisited.
E. Bossolini, R. Edwards, P. A. Glendinning, M. R. Jeffrey, S. Webber
(2016) Regularization by External Variables.
Paul Glendinning (2016) Less is More I: a pessimistic view of piecewise smooth bifurcation theory.
Paul Glendinning (2016) Less is More II: an optimistic view of piecewise smooth bifurcation theory.
Publications: articles and books
-  Paul Glendinning (2016)
Geometry of refractions and reflections through a biperiodic medium, SIAM J. Appl. Math., 76(4), 1219–1238
-  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.
-  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
-  Paul Glendinning (2016) Classification of Boundary
Equilibrium Bifurcations of planar Filippov systems, Chaos 26, 013108; http://dx.doi.org/10.1063/1.4940017
-  Paul Glendinning (2015) Bifurcation from stable fixed point to $N$-dimensional attractor in the border collision normal form, Nonlinearity 28(10): 3457-3464.
-  N. J. Higham (Editor) Princeton Companion to Applied Mathematics, Princeton, 2015 (Associate Editor and Contributor).
-  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]
-  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.
-  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
-  P. Glendinning (2014) Invariant Measures for the n-Dimensional Border Collision Normal Form, IJBC 24 (12) 1450164 DOI: 10.1142/S0218127414501648
-  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)
-  V. Botella-Soler and P.Glendinning (2014) Hierarchy and polysynchrony in an adaptive network. Phys. Rev. E 89 062809.
-  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.
-  Paul Glendinning (2014) The Border Collision Normal Form with Stochastic Switching Surface. SIAM J. Applied Dynamical Systems 13, 181-193
-  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.
-  50 Visions of Mathematics (2014) Ed. Sam Parc [PG is the ‘P’], OUP.
-  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
-  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]
-  P. Glendinning and L.A. Smith (2013) Lacunarity and period-doubling, Dyn. Syst. IJ, DOI:10.1080/14689376.2012.755496 [11 pages]
-  P. Glendinning, P. Kowalczyk and A.B. Nordmark (2012) Attractors near grazing-sliding bifurcations, Nonlinearity 25 1867--1885.
-  P. Glendinning (2012) Maths In Minutes, Quercus. [410 small pages]
-  V. Botella-Soler and P. Glendinning (2012) Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems, EPL, 97, 50004.
-  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
-  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.
-  P. Glendinning (2011) Two Ball Newton Cradle, Phys. Rev. E, 84:067201
-  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.
-  P. Glendinning and P. Kowalczyk (2011) ‘Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems.’ Chaos. 21:023126 [11 pages].
-  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]
-  P. Glendinning and C.H. Wong (2011) Two-dimensional attractors in the border-collision normal form, Nonlinearity, 24, 995-1010.
-  P. Glendinning (2010) Bifurcations of snap-back repellers with application to the border-collision normal form', Int. J. Bifn. Chaos 20, 479-489
-  P. Glendinning and P. Kowalczyk (2010) 'Micro-chaotic dynamics due to digital sampling in hybrid systems of Filippov type', Physica D, 239, 58-71
-  P. Glendinning and P. Kowalczyk (2009) 'Dynamics of a hybrid thermostat model with discrete sampling time control', Dynamical Systems IJ, 23 343-360.
-  P. Glendinning, T. Jaeger and J. Stark (2009) `Strangely dispersed minimal sets in the quasiperiodically forced Arnold circle map', Nonlinearity 22 835-854
-  '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).
-  ‘How chaotic are strange non-chaotic attractors?’ (2006) Nonlinearity, 19, 2005-2023 (with G.Keller and T.Jaeger).
-  'Routes to Chaos' (2005) Encyclopedia of Nonlinear Science
Ed A. Scott, Routledge, New York pp. 814-817.
-  'Invariant manifolds and sets' (2005) Encyclopedia of Nonlinear Science
Ed A. Scott, Routledge, New York pp. 465-467.
-  'Henon map' (2005) Encyclopedia of Nonlinear Science
Ed A. Scott, Routledge, New York pp. 403-406.
-  `The non-smooth pitchfork bifurcation' (2004)
Discrete and Continuous Dynamical Systems B 4, 457-464
(pdf file, 1.5M)
-  `The mathematics of motion camouflage' (2004) Proc. Roy. Soc. (London)
Series B 271 477-481 available as a pdf file.
-  `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,
This note is available as a
-  `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
-  `Global attractors of pinched skew products' (2002) Dyn. Syst. IJ
17 287-297. This paper is available as a
-  `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.
-  `Imperfect Homoclinic Bifurcations' (2001) Phys. Rev. E 64 036208
(8 pages) (with J. Abshagen and
-  `Multistability in the quasiperiodically forced circle
map' (2001) IJBC 11 3085-3105 (with H. Osinga, U. Feudel and J. Wiersig).
has its very own
web site which has loads of pretty pictures (in colour) and explanatory text.
-  `Unique representations of real numbers in non-integer bases' (2001)
Math. Res. Lett. 8 535-543 (with N. Sidorov).
A dvi file is available.
-  `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.
-  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.
-  `Milnor attractors and topological attractors in a piecewise
linear map' (2001) Nonlinearity 14 239-258. Available as a
-  `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
-  `Transitivity and blowout bifurcations in a class of globally
coupled maps' (1999) Phys. Lett. A 264 303-310
(pdf -- text only)
-  `The stability boundary of synchronized states in globally coupled
dynamical systems' (1999) Phys. Lett. A 259 129-134
-  `Fine structure of mode-locked regions of the quasi-periodically
forced circle map' (1999) Phys. Lett. A 257 65-69 (with J. Wiersig)
-  `Towards a quasi-periodic mean field theory of globally coupled
oscillators' (1999) Phys. Lett. A 251 297-302 (with M. Banaji)
-  `Intermittency and strange nonchaotic attractors in quasi-periodically
forced circle maps' (1998) Phys. Lett. A 244 545-550
-  `Melnikov analysis of chaos in a simple epidemiological model' (1997)
J. Math. Biol. 35 359-373 (with L.P. Perry)
-  `Bifocal homoclinic bifurcations' (1997) Physica D 102 1-14
(with C.R. Laing)
-  `Inaccessible attractors of weakly dissipative systems' (1997)
Nonlin. 10 507-522
-  `Differential equations with bifocal homoclinic orbits' (1997)
Intl. J. Bifn. & Chaos 727-37
-  `Shilnikov's saddle-node bifurcation' (1996) Intl. J. Bifn.
& Chaos 6 1153-1160 (with C. Sparrow)
-  `Zeros of the kneading invariant and topological entropy for
Lorenz maps' (1996) Nonlin. 9 999-1014 (with T. Hall)
-  `A homoclinic hierarchy' (1996) Phys. Lett. A 211 155-160
(with C.R. Laing)
-  `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
-  `Locating bifurcations in quasiperiodically forced systems' (1995)
Phys. Lett. A 200 17-26 (with P.R. Chastell and J. Stark)
-  Stability, Instability and Chaos: an introduction to the theory
of nonlinear differential equations (1994) 388 pages, CUP
-  `Island chain models and gradient systems' (1994)
J. Math. Biol. 32 171-178
-  `Prime and renormalisable kneading invariants and the dynamics of
expanding Lorenz maps' (1993) Physica D 62, 22-50 (with C. Sparrow)
-  `Travelling waves with spatially resonant forcing: bifurcations of a
modified Landau equation' (1993) Int. J. Bifn. & Chaos 3, 1447-1455 (with
-  `The anharmonic route to chaos: kneading theory' (1993) Nonlin.
-  `Robust new routes to chaos in differential equations' (1992)
Phys. Lett. A 168 40-46
-  `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
-  `Renormalisation between classes of maps' (1990) Phys. Lett. A
145 109-112 (with J.E. Los and C. Tresser)
-  `Explicit renormalisation of some piecewise linear maps' (1990)
Physica D 44 149-167 (with D. Veitch)
-  `Topological conjugation of Lorenz maps to $\beta$-transformations'
(1990) Math. Proc. Camb. Phil. Soc. 107, 401-413
-  `Global structure of homoclinic bifurcations: a combinatorial
approach' (1989) Phys. Lett. A 141 391-396
-  `Subsidiary bifurcations near bifocal homoclinic orbits' (1989)
Math. Proc. Camb. Phil. Soc.105 597-605
-  `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)
-  `The gluing bifurcation I: symbolic dynamics of the closed curves' (1988)
Nonlinearity 1, 203-214 (with J.M. Gambaudo and C. Tresser)
-  `Global bifurcations in flows' (1988) in
New directions in dynamical systems eds. T. Bedford and J. Swift, CUP
-  `Asymmetric perturbations of Lorenz-like equations' (1987) Dyn.Stab. Syst.
-  `Travelling waves near isolated double-pulse solutions of nerveaxon equations',
(1987) Phys. Lett. A 121, 411-413
-  `Homoclinic bifurcations in ordinary differential equations' (1987)
in Chaos in biological systems, eds. H. Degn, A.V. Holden and
L. Olson, Plenum, New York
-  `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)
-  `T-points: a codimension two heteroclinic bifurcation' (1986)
J. Stat. Phys. 43, 479-488 (with C. Sparrow)
-  `Stable cycles with complicated structures' (1985) J. Physique Lett.
46, L653-L658 (with J.M. Gambaudo and C. Tresser)
-  `Heteroclinic loops leading to hyperchaos' (1985) J. Physique Lett.
46, L347-L352 (with J.M. Gambaudo and C. Tresser)
-  `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)
-  `The rotation interval as a computable measure of chaos' (1984)
Phys. Lett. A 105, 97-100 (with J.M. Gambaudo and C. Tresser)
-  `Bifurcations near homoclinic orbits with symmetry' (1984) Phys.Lett. A
-  `Local and global behaviour near homoclinic orbits' (1984) J. Stat. Phys. 35,
645-696 (with C. Sparrow)
Lecture notes/theses/books in progress
-  `Homoclinic bifurcation' (1985) Ph.D. thesis, University of Cambridge
-  `Introduction to computational dynamics` (1988) lecture notes,
112 pages, for ICTP Summer School on Dynamical Systems, Trieste, 1988
(with J. Stark)
-  Chaos and routes to chaos in Lorenz maps (1992) an essay for the
Adams Prize (223 pages), to become a book
-  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)
-  Bifurcation Theory: codimension one bifurcations (1996) lecture
notes for Nonlinear Mathematics School, Bristol
-  `Maps of the Circle' in One dimensional dynamics, (1996)
TEMPUS Lecture Notes volume 14
-  Mathematical models in economics (1998) Queen Mary and Westfield
College Lecture Notes, 115 pages, to become a book
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