Robert MacKay Professor of Mathematics, Director of Mathematical Interdisciplinary Research at Warwick Office: C1.12 Phone: +44 (0)24 765 22218 Email: R dot S dot MacKay at warwick dot ac dot uk

Teaching Responsibilities 2024/25:

Term 2: MA4H0 Applied Dynamical Systems, and TCC Thermal Economics

ThermoEconomics Talk (13 Dec 2021)

and ThermoEconomics Paper (6 Oct 2023)

Mathematics for Fusion Power TCC lectures

MA4K9 & MSc project topics

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Research Interests:
Dynamical systems, mathematical physics, and complexity science; applications to physics, biology, chemistry, engineering, economics, finance, social science.

Notably, Simons collaboration on Hidden Symmetry and Fusion Energy

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CV and publication list March 2021

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Some publications (not updated since 2011!) (read my CV instead, which I update more frequently):

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

Some research grants (but has not been updated since 2012!):

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

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 .