- `Lacunarity and period-doubling', (1999) submitted to Phys. Lett. A (with L.A. Smith) Text only is available as a pdf file.

See Manchester EPrints for recent preprints and papers.

- [69] P. Glendinning (2012)
*Maths In Minutes,*Quercus. - [68] 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. - [67] 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. - [66] 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].
- [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] 'Dynamics of a hybrid thermostat model with
discrete sampling time control', (2009) Dynamical Systems IJ,
**23**343-360, with P. Kowalczyk. - [59] 'Border collision bifurcations, snap-back repellers, and chaos', Phys. Rev. E 79, 025202(R) (2009) [4 pages], prerprint from Manchester eprints.
- [58] `Strangely dispersed minimal sets
in the quasiperiodically forced Arnold circle map',
Nonlinearity
**22**835-854, with T. Jaeger and J. Stark (pdf file) - [57] `How chaotic are strange nonchaotic
attractors?' (2006) Nonlinearity,
**19**2005-2022 with T. Jaeger and G. Keller. - [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) pdf file here. - [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

- `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: Newtonian Choreographies, Mathematics Today,
December 2002,
**38**184-185. - View from the Pennines: Making Connections, Mathematics Today,
February 2003,
**39**26-27. - View from the Pennines: Ideal Knots, Mathematics Today,
April 2003,
**39**60-61. - View from the Pennines: Almost Automorphisms, Mathematics Today,
June 2003,
**39**85-86. - View from the Pennines: Non-trivial Pursuits, Mathematics Today,
August 2003,
**39**118-120. - View from the Pennines: Analysis on Time Scales, Mathematics Today,
October 2003,
**39**156-159. - View from the Pennines: Sticky waves, Mathematics Today,
December 2003,
**39**198-199. - View from the Pennines: On Art and Causal Sets, Mathematics Today,
February 2004,
**40**32-33. - View from the Pennines: Pattern Complexity, Mathematics Today,
April 2004,
**40**65-66.To download the View from the Pennines articles go to the View from the Pennines homepage.

Back to my home page