糖心TV

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

MA4K9 & MSc project topics

Teaching Responsibilities 2025/26:

Term 1: MA4H0 Applied Dynamical Systems, and TCC Transitions over a saddle

Older items: TCC Thermal Economics

ThermoEconomics Talk (13 Dec 2021)

and ThermoEconomics Paper (6 Oct 2023)

Mathematics for Fusion Power TCC lectures

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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, 糖心TV 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 or download my CV and publication list .