On leave 2015/16
Professor of Mathematics
Director of MathSys CDT
Teaching Responsibilities 2015/16:
2015/6 MA469 project topics
Dynamical systems, mathematical physics, and complexity science
Publications from 2003 (plus some old ones)(not updated since 2011):
MacKay RS, Stark J, Lectures on Orbits of Minimal Action for Area-preserving Maps, Warwick Maths Institute preprint 1985 (corrected 1989)
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 18 (2008) 615-666.
Pelinovsky D, Schneider G, MacKay RS, Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential , Commun Math Phys 284 (2008) 803-831.
MacKay RS, Mode conversion in the cochlea? , subm to J Roy Soc Interface, Aug 2008 (revised version of IHES preprint, June 2006)
MacKay RS, Nonlinearity in complexity science , Nonlinearity 21 (2008) T273-81
MacKay RS, Langevin equation for slow degrees of freedom of Hamiltonian systems , in "Nonlinear Dynamics and Chaos", eds M Theil, J Kurths, MC Romano, G Karolyi, A Moura (Springer, 2010) 89-102.
RC Ball, M Diakonova, RS MacKay, Quantifying emergence in terms of persistent mutual information, Adv Complex Sys 13 (2010) 327-338.
RS MacKay, Existence of invariant circles for infinitely renormalisable area-preserving maps, in: ``Dynamics, Games and Science vol. I", ed A Pinto (Springer, 2011), 629-635.
MacKay RS, Robustness of Markov processes on large networks , J Difference Eqns & Applns 17 (2011) 1155-1167.
R MacKay, C Rourke, Natural flat observer fields in spherically-symmetric space-times, subm to Gen Rel Grav
M Diakonova, RS MacKay, Mathematical examples of space-time phases, to appear in Int J Bif Chaos
RS MacKay, C Rourke, Natural observer fields and redshift, to appear in J Cosmol
J Thornby, RS MacKay, R Sanders, MA Williams, Mathematical principles for the design of isostatic mount systems for dynamic structures, subm to IEEE Trans Robot
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 - Mar 11)
EPSRC, The Mathematics of complexity science and systems biology (Symposium year) (Sep 09 - Aug 11)
LMS, Complex System Dynamics network, Jan 09 - Sep 11
Sloan Foundation, Management of Complex Systems, Jan 12 - Dec 13