Preprints, papers and books

Preprints/in preparation/to appear

• `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.

Publications: articles and books

• [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 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

• `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.