Robert MacKay Professor of Mathematics   Director of Mathematical Interdisciplinary Research Director of Centre for Complexity Science Office: B2.05 Phone: +44 (0)24 765 22218 Email: R dot S dot MacKay at warwick dot ac dot uk

Research Interests: Dynamical systems, mathematical physics, and complexity science

Teaching: 2009/10, Term 1: Access Grid PhD module on Topics in Complexity Science (16 hours), based on the MSc module MA5Q3 Complexity Science I taught in 06/07.  Click tab on left for webpage.

Publications from 2003:

Hunt T J, MacKay R S.  Anosov parameter values for the triple linkage and a physical system with a uniformly chaotic attractor. Nonlinearity 16 (2003) 1499-1510

Bishnani Z, MacKay R S. Safety criteria for aperiodically forced systems. Dynamical Systems 18 (2003) 107-129

Bolotin S, MacKay RS, Isochronous potentials, in Localization and energy transfer in nonlinear systems, eds Vazquez L, MacKay RS, Zorzano M-P (World Sci, 2003) 217-224

Catarino NR, MacKay RS, Quantum statistical mechanics of Frenkel-Kontorova models, in Localization and energy transfer in nonlinear systems, eds Vazquez L, MacKay RS, Zorzano M-P (World Sci, 2003) 315-9 

Baesens C, MacKay RS, A novel preserved partial order for cooperative networks of overdamped second order units, and application to tilted Frenkel-Kontorova chains, Nonlinearity 17 (2004) 567-580 

Bialy M, MacKay RS, Symplectic twist maps without conjugate points, Israel J Math 141 (2004) 235-248 

Berger A, MacKay RS, Rothos VM, A criterion for non-persistence of travelling breathers for perturbations of the Ablowitz-Ladik lattice, Discr Cont Dyn Sys B 4 (2004) 911-920 

MacKay RS, Slow manifolds, in Energy localisation and transfer, eds Dauxois T, Litvak-Hinenzon A, MacKay RS, Spanoudaki A (World Sci, 2004) 149-192 

Theodorakopoulos N, Peyrard M, MacKay RS, Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system, Phys Rev Lett 93 (2004) 258101 (4 pages) 

Koukouloyannis V, MacKay RS, Existence and stability of 3-site breathers in a triangular lattice, J Phys A 38 (2005) 1021-30

MacKay RS, Chaos in three physical systems, in Equadiff 2003, eds Dumortier F et al (World Sci, 2005) 59-72 

MacKay RS, Indecomposable coupled map lattices with non-unique phase, in Dynamics of coupled map lattices and of related spatially extended systems, eds Chazottes J-R, Fernandez B, Lect Notes in Phys 671 (Springer, 2005) 65-94 

Catarino NR, MacKay RS, Renormalization and quantum scaling of Frenkel-Kontorova models , J Stat Phys 121 (2005) 995-1014 

Baesens C, MacKay RS, Discommensuration theory for Frenkel-Kontorova models and shadowing, Physica D 216 (2006) 179-184 

MacKay RS, MacKay DJC, Ergodic pumping: a mechanism to drive biomolecular conformation changes , Physica D 216 (2006) 220-234 

Bolotin S, MacKay RS. Nonplanar second species periodic and chaotic trajectories for the circular restricted three-body problems. Cel Mech Dyn Astron 94 (2006) 433 - 449

Pinheiro D, MacKay RS, Interaction of two charges in a uniform magnetic field I planar case, Nonlinearity 19 (2006) 1713-45 

MacKay RS. Cerbelli and Giona's Map Is Pseudo-Anosov and Nine Consequences . J.Nonlinear Sci 16 (2006) 415-434

Baesens C, MacKay RS, Resonances for weak coupling of the unfoding of a saddle-node periodic orbits with an oscillator , Nonlinearity 20 (2007) 1283-98 

Celletti A, MacKay RS, Regions of non-existence of invariant tori for spin-orbit models , Chaos 17 (2007) 043119 (12 pages) 

MacKay RS, Parameter-dependence of Markov processes on large networks , in Proc ECCS'07, eds Jost J et al (on CD)

Pinheiro D, MacKay RS, Some properties of the dynamics of two interacting particles in a uniform magnetic field, in Symmetry and Perturbation theory, eds Gaeta G, Vitolo R, Walcher S (World Sci, 2007) 267-8 

Yamapi R, MacKay RS, Stability of synchronisation in a shift-invariant ring of mutually coupled oscillators, Discr Conts Dyn Sys B 10 (2008) 973-996.

MacKay RS, A steady mixing flow with no-slip boundaries , in: Chaos, complexity and transport, eds Chandre C, Leoncini X, Zaslavsky GM (World Sci, 2008) 55-68.

Pinheiro D, MacKay RS, Interaction of two charges in a uniform magnetic field: II spatial case , J Nonlin Sci (2008) on-line first

Pelinovsky D, Schneider G, MacKay RS, Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential , Commun Math Phys, in press

MacKay RS, Mode conversion in the cochlea? , subm to J Roy Soc Interface, Aug 2008 (revised version of IHES preprint, June 2006)

MacKay RS, Langevin equation for slow degrees of freedom of Hamiltonian systems , subm to special issue of J Roy Soc Interface on Mathematics in the Science of Complex Systems, Aug 2008 (revised version of paper presented at model Reduction, Leicester, Aug 2007)

MacKay RS, Nonlinearity in complexity science , invited submission for Open Problems series, Nonlinearity, Aug 2008 

MacKay RS, Robustness of Markov processes on large networks , subm to Probability Theory & Rel Fields, Aug 2008 (revised  version of ECCS'07 paper)

Recent research grants:

INTAS, Chaotic Motion and Stability in Conservative and Near-Conservative systems (01.07.2001 - 31.8.2003)

London Mathematical Society, Young Russian mathematician grant/Vladimir Ten (1.10.02 - 30.11.02)

EC/Marie Curie, Tunneling Quantum Roto-Breathers/Anna Litvak-Hinenzon (1.2.2002 - 28.8.2004) 

Royal Society, System Dynamics/Mohammad Ghaffari Saadat (21/09/2003- 20/12/2003)

Royal Society, International Congress on Dynamical Systems (19/07/2005 - 18/09/2005)

Royal Society, Synchronisation in Networks of Dynamic Units/Rene Yamapi (17/09/2006 - 10/12/2006)

EPSRC, Localised Modes in Non-Linear Lattices/Dmitry Pelinovsky (01/10/2006 - 31/12/2006)

EPSRC, Doctoral training centre in Complexity Science (1.10.2006 - 30.9.2014) 

LMS, From nonlinear dynamics to systems biology (Dec 2008)

TSB and Metris UK, Calibration and motion control of a robotic arm (Sep 08 - Aug 2010)

For more information and further publications see an old version (which was maintained only sporadically after Sept 2005) of Robert MacKay's homepage or download my CV and publication list .