Preprints, papers and books
Preprints/in preparation/to appear
Publications: articles and books
-  P. Glendinning (2012) Maths In Minutes, Quercus.
-  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.
-  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. Kowalczyk, P. Glendinning, M. Brown, G. Medrano-Cerda, H. Dallali, J. Shapiro (2011)
‘Modelling human balance using switched systems with linear feedback control.’,
J Roy Soc Interface. June 22. [Epub ahead of print].
-  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.
-  'Dynamics of a hybrid thermostat model with
discrete sampling time control', (2009) Dynamical Systems IJ, 23 343-360, with P. Kowalczyk.
-  'Border collision bifurcations, snap-back repellers, and chaos',
Phys. Rev. E 79, 025202(R) (2009) [4 pages], prerprint from Manchester eprints.
-  `Strangely dispersed minimal sets
in the quasiperiodically forced Arnold circle map',
Nonlinearity 22 835-854, with T. Jaeger and J. Stark (pdf file)
-  `How chaotic are strange nonchaotic
attractors?' (2006) Nonlinearity, 19 2005-2022 with T. Jaeger and G. Keller.
-  '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
T. Mullin) pdf file here.
-  `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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