Robert Sinclair MacKay

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Mathematics

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#5122

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Measure Theory

#1707

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#2098

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Mathematics

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According to Wikipedia, Robert Sinclair MacKay is a British mathematician and professor at the University of Warwick. He researches dynamical systems, the calculus of variations, Hamiltonian dynamics and applications to complex systems in physics, engineering, chemistry, biology and economics.

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Robert Sinclair MacKay's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators (1994) (774)
INTRODUCTION TO THE MODERN THEORY OF DYNAMICAL SYSTEMS (Encyclopaedia of Mathematics and its Applications 54) (1997) (382)
Transport in Hamiltonian Systems (1984) (288)
Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos (1991) (217)
Renormalisation in Area-Preserving Maps (1993) (210)
A renormalization approach to invariant circles in area-preserving maps (1983) (181)
Frontiers of chaotic advection (2014) (156)
Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices (1997) (153)
Resonances in area-preserving maps (1987) (139)
STOCHASTICITY AND TRANSPORT IN HAMILTONIAN SYSTEMS (1984) (138)
Stability of water waves (1986) (127)
Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators (1997) (118)
Rotation vectors and entropy for homeomorphisms of the torus isotopic to the identity (1991) (109)
Multistability in networks of weakly coupled bistable units (1995) (109)
Solitary waves in a chain of beads under Hertz contact (1999) (95)
Universal Behaviour in Families of Area-Preserving Maps (1981) (94)
Breathers on a diatomic FPU chain (1997) (93)
Greene's residue criterion (1992) (90)
Transport in 3D volume-preserving flows (1994) (84)
Cantori for symplectic maps near the anti-integrable limit (1992) (82)
Transition to topological chaos for circle maps (1996) (76)
Linear stability of symplectic maps (1987) (76)
Converse KAM theory for symplectic twist maps (1989) (76)
Hamiltonian dynamical systems : a reprint selection (1987) (75)
Some flesh on the skeleton: The bifurcation structure of bimodal maps (1987) (72)
Boundary circles for area-preserving maps (1986) (70)
Challenges in complex systems science (2012) (68)
Discrete breathers: classical and quantum (2000) (61)
Stability of discrete breathers (1998) (60)
Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models (1992) (60)
Movement of eigenvalues of Hamiltonian equilibria under non-Hamiltonian perturbation (1991) (59)
Flux over a saddle (1990) (56)
GRADIENT DYNAMICS OF TILTED FRENKEL-KONTOROVA MODELS (1998) (51)
Locally most robust circles and boundary circles for area-preserving maps (1992) (50)
Coupled map lattices with phase transition (2000) (47)
Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family (1992) (46)
Fractal boundary for the existence of invariant circles for area-preserving maps: Observations and renormalisation explanation (1989) (46)
Boundary of topological chaos for bimodal maps of the interval (1988) (46)
Effective Hamiltonian for travelling discrete breathers (2002) (45)
Energy localisation and transfer (2004) (44)
Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant ori (1988) (44)
Multibump orbits near the anti-integrable limit for Lagrangian systems (1997) (42)
Transition to chaos for area-preserving maps (1986) (42)
Periodic and Chaotic Trajectories of the Second Species for the n-Centre Problem (2000) (41)
Resonance regions for families of torus maps (1989) (40)
Exponential localization of linear response in networks with exponentially decaying coupling (1997) (40)
Dynamics of Relative Phases: Generalised Multibreathers (2001) (38)
Linear Stability of Periodic Orbits in Lagrangian Systems (1983) (38)
On generation-integrated energy storage (2015) (37)
Markov shifts in the He´non family (1991) (37)
Nonlinearity in complexity science (2008) (37)
Topology from time series (1993) (37)
Discrete breathers and Anderson modes: two faces of the same phenomenon? (1999) (36)
A criterion for non-existence of invariant tori for Hamiltonian systems (1989) (36)
Anosov parameter values for the triple linkage and a physical system with a uniformly chaotic attractor (2003) (34)
Universal small-scale structure near the boundary of siegel disks of arbitrary rotation number (1987) (32)
Scaling exponents at the transition by breaking of analyticity for incommensurate structures (1991) (31)
A novel preserved partial order for cooperative networks of units with overdamped second order dynamics, and application to tilted Frenkel–Kontorova chains (2004) (30)
Period doubling for bimodal maps: a horseshoe for a renormalisation operator (1988) (28)
Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system. (2004) (28)
Flux and differences in action for continuous time Hamiltonian systems (1986) (27)
Existence and stability of 3-site breathers in a triangular lattice (2005) (27)
Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic Potential (2007) (27)
Complicated dynamics from simple topological hypotheses (2001) (26)
A simple proof of Denjoy's theorem (1988) (25)
Improved proof of existence of chaotic polaronic and bipolaronic states for the adiabatic Holstein model and generalizations (1994) (24)
Cantori for multiharmonic maps (1993) (24)
Transition to chaos for two-frequency systems (1984) (23)
Pseudo-Anosov homeomorphisms on a sphere with four punctures have all periods (1992) (23)
Nonplanar Second Species Periodic and Chaotic Trajectories for the Circular Restricted Three-Body Problem (2006) (23)
Localised modes on localised equilibria (1998) (22)
Local Activity Principle: The Cause of Complexity and Symmetry Breaking (2015) (22)
Quantifying Emergence in Terms of Persistent Mutual Information (2010) (21)
Consequences of contractible geodesics on surfaces (1998) (21)
How directed is a directed network? (2020) (21)
Symplectic twist maps without conjugate points (2003) (20)
Equivariant universality classes (1984) (19)
Calculation of linear stability boundaries for equilibria of Hamiltonian systems (1987) (18)
A Classification of Braid Types for Diffeomorphisms of Surfaces of Genus Zero with Topological Entropy Zero (1990) (18)
The physics of gamma-ray bursts (2020) (17)
Indecomposable coupled map lattices with non-unique phase (2005) (17)
Langevin equation for slow degrees of freedom of Hamiltonian systems (2010) (17)
Mathematical Examples of Space-Time Phases (2011) (16)
Hamiltonian Dynamical Systems (2020) (16)
A variational principle for invariant odd-dimensional submanifolds of an energy surface for Hamiltonian systems (1991) (15)
Isochronous Potentials (2000) (15)
Introduction to the dynamics of area–preserving maps (1987) (15)
The one to two-hole transition for cantori (1994) (15)
Recent progress and outstanding problems in Hamiltonian dynamics (1995) (14)
Cerbelli and Giona's Map Is Pseudo-Anosov and Nine Consequences (2006) (14)
Hyperbolic cantori have dimension zero (1987) (14)
Simple Resonance Regions of Torus Diffeomorphisms (1991) (14)
Stability of Equilibria of Hamiltonian Systems (2020) (13)
Badly ordered orbits of circle maps (1984) (12)
Rotation interval from a time series (1987) (12)
Discrete breathers in disordered media (1998) (11)
Robustness of Markov processes on large networks (2011) (11)
Ergodic pumping: A mechanism to drive biomolecular conformation changes (2006) (11)
Dynamical Systems and Numerical Analysis. By A. Stuart & R. Humphries. Cambridge University Press, 1996. 685 pp. ISBN 0-521-49672-1. £40. (1997) (11)
A Classification of braid types for periodic orbits of diffeomorphisms of surfaces of genus one with topological entropy zero (1991) (11)
Diffusing through spectres: ridge curves, ghost circles and a partition of phase space (1993) (10)
Cantori for symplectic maps (1990) (10)
Badly ordered periodic orbits of the standard map (1986) (10)
Interaction of Two Charges in a Uniform Magnetic Field: II. Spatial Problem (2008) (10)
INTRODUCTION TO THE QUALITATIVE THEORY OF DYNAMICAL SYSTEMS ON SURFACES (Translations of Mathematical Monographs 153) By S. Kh. Aranson, G. R. Belitsky and E. V. Zhuzhoma: 325 pp., US$129.00, ISBN 0 8218 0369 7 (American Mathematical Society, 1996) (1998) (10)
Islets of stability beyond period doubling (1982) (9)
An approximation to the critical commuting pair for breakup of noble tori (1985) (9)
ALGEBRAIC LOCALISATION OF LINEAR RESPONSE IN NETWORKS WITH ALGEBRAICALLY DECAYING INTERACTION, AND APPLICATION TO DISCRETE BREATHERS IN DIPOLE-DIPOLE SYSTEMS (1999) (9)
A criterion for non-persistence of travelling breathers for perturbations of the Ablowitz-Ladik lattice (2004) (9)
Abrupt bifurcations in chaotic scattering: view from the anti-integrable limit (2013) (9)
Approximate renormalization with codimension-one fixed point for the break-up of some three-frequency tori (2000) (9)
A Renormalisation Approach to Invariant Circles in Area-Preserving Maps (2020) (9)
Evaluation of an approximate renormalisation scheme for area-preserving maps (1989) (8)
Complexity Science: The Warwick Master's Course (2013) (8)
Finite coherence length for equilibrium states of generalized adiabatic Holstein models (1997) (8)
Optimal scheduling in a periodic environment (2000) (7)
Phase Diagrams of Majority Voter Probabilistic Cellular Automata (2015) (7)
Chaotic Properties of Subshifts Generated by a Nonperiodic Recurrent Orbit (1999) (7)
BIOPHYSICAL LIMITATIONS ON DEEP DIVING: SOME LIMITING PERFORMANCE EXPECTATIONS. (1963) (7)
Rotationally-ordered periodic orbits for multiharmonic area-preserving twist maps (1994) (7)
Instability of vortex streets (1987) (7)
PHONON SCATTERING BY LOCALIZED EQUILIBRIA OF NONLINEAR NEAREST-NEIGHBOR CHAINS (1997) (6)
Stability of synchronization in a shift-invariant ring of mutually coupled oscillators (2008) (6)
Optimal strategies for operating energy storage in an arbitrage or smoothing market (2016) (6)
Cases on Criminal Law (1964) (6)
A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control (2017) (6)
Optic Discrete Breathers in Euclidean Invariant Systems (2000) (5)
Period doubling in area preserving maps (1993) (5)
RENORMALIZATION METHODS: CRITICAL PHENOMENA, CHAOS, FRACTAL STRUCTURES (2000) (5)
Mode-locking and rotational chaos in networks of oscillators: A mathematical framework (1994) (5)
Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow (2018) (5)
An unethical optimization principle (2019) (5)
Effect of temperature on polaronic and bipolaronic structures of the adiabatic Holstein model (1996) (5)
A New Paradigm in Quantum Chaos: Aubry's Theory of Equilibrium States for the Adiabatic Holstein Model (1993) (5)
Transition of the phase-resetting map for kicked oscillators (1991) (4)
Defects in solids, large molecules and space structures (2000) (4)
An extension of Zeeman's notion of structural stability to non-invertible maps (1991) (4)
Optimal strategies for operating energy storage in an arbitrage market (2014) (4)
Renormalization and Quantum Scaling of Frenkel–Kontorova Models (2005) (3)
CHAOS IN THREE PHYSICAL SYSTEMS (2005) (3)
The classical statistical mechanics of Frenkel-Kontorova models (1995) (3)
Renormalisation of bicritical circle maps (1994) (3)
Parameter-dependence of Markov processes on large networks (2008) (3)
Implanted transmitters and body fluid permeability. (1965) (3)
Level Set Methods. By J. A. Sethian. Cambridge University Press, 1996. 218 pp. ISBN 052187202 9. £27.95 (1997) (2)
Continuity of the phonon gap (1993) (2)
Some Reflections on the New Canadian Criminal Code (1958) (2)
ErratumTransition to topological chaos for circle maps (1988) (2)
Variational properties of a nonlinear elliptic equation and rigidity (1999) (2)
An Appraisal of the Ruelle-Takens Route to Turbulence (1991) (2)
A natural 4-parameter family of covariance functions for stationary Gaussian processes (2018) (2)
The English conflict of laws (1957) (2)
Towards a spectral proof of Riemann's hypothesis (2017) (2)
Complexity Science: Space-time phases (2013) (2)
Introduction to renormalisation (1993) (2)
QUANTUM STATISTICAL MECHANICS OF FRENKEL-KONTOROVA MODELS (2003) (2)
Thermodynamics kept simple – a molecular approach: what is the driving force in the world of molecules?, by Roland Kjellander (2016) (2)
Excited states in the adiabatic Holstein model (1998) (2)
THERMODYNAMICS OF CHAOS AND ORDER (Pitman Monographs and Surveys in Pure and Applied Mathematics 90) (1999) (2)
Exponentially Small Residues Near Analytic Invariant Circles (1991) (1)
Existence of Invariant Circles for Infinitely Renormalisable Area-Preserving Maps (2011) (1)
Inference of modes for linear stochastic processes (2019) (1)
Period Doubling as a Universal Route to Stochasticity (2017) (1)
Mathematical principles for the design of isostatic mount systems for dynamic structures (2015) (1)
Recent advances in biotelemetry and their applications to measurements of pressure and electrical changes in the oviduct in vivo. (1974) (1)
Simulation, modelling and development of the metris RCA (2009) (1)
Cerbelli and Giona ’ s map is pseudo-Anosov and 9 consequences (1)
Temperature Sensing and Transmission (1993) (1)
Discommensuration theory and shadowing in Frenkel–Kontorova models (2006) (1)
Many-body quantum mechanics (2002) (1)
Corrigendum: Simplest bifurcation diagrams for monotone families of vector fields on a torus (2018 Nonlinearity 31 2928) (2022) (1)
Preface - Serge Aubry (2006) (1)
Coordinate change eigenvalues for bimodal period doubling renormalisation (1994) (1)
Stability and chaotic advection in the eccentric Taylor problem (1991) (1)
Evaluation of an approximate renormalization scheme for area-preserving maps (1989) (1)
Complex systems techniques for cyber-physical systems: position paper (2014) (1)
Appendix 4. Laboratory Experiment on Transmitter Construction (1993) (0)
Modern thermodynamics for chemists and biochemists (2020) (0)
Plastics and Other Materials (1993) (0)
Frequency and Antenna Selection (1993) (0)
Characteristics, accuracy and reverification of robotised articulated arm CMMs (2010) (0)
Mathematical Structures in Continuous Dynamical Systems. By E. VAN GROESEN & E. M. DE JAGER. North Holland, 1994. 617 pp. ISBN 0 444 821 511. Dfl 295 or U173.50. (1996) (0)
Draft to be submitted to Nonlinearity EXAMPLE OF SIMPLEST BIFURCATION DIAGRAM FOR A MONOTONE FAMILY OF VECTOR FIELDS ON A TORUS CLAUDE BAESENS, MARC HOMS-DONES AND ROBERT S. MACKAY (2022) (0)
Review of Theories of molecular reaction dynamics : the microscopic foundations of chemical kinetics, by Henriksen, N.E. and Hansen, F.Y. (2008) (0)
Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow (2018) (0)
A new stochastic framework for ship capsizing (2021) (0)
Nonarea-preserving directions from area-preserving golden circle fixed points (1993) (0)
Persistence of spectral projections for stochastic operators on large tensor products (2022) (0)
Probability on Graphs: Random Processes on Graphs and Lattices, by G. Grimmett (2012) (0)
Survey of Hamiltonian Dynamics (2020) (0)
Introduction to area preserving maps (1993) (0)
Complexity miniproject report (2012) (0)
Chaos in Systems with Noise (Tomasz Kapitaniak) (1991) (0)
The Multiplicity of Bifurcations for Area-Preserving Maps (1994) (0)
Exploring the possibility of following the movements of a bird from an artificial earth satellite (1974) (0)
Introduction to accelerator dynamics (2019) (0)
The unknowable by Gregory Chaitin (1999) (0)
Cerbelli and Giona ’ s map is pseudo - (2005) (0)
Appendix 5. Phaselock Loop Receiver (1993) (0)
Normal Hyperbolicity for Non-autonomous Oscillators and Oscillator Networks (2020) (0)
Physics of Biological Oscillators: Outlook (2021) (0)
Appendix 1. Antenna Turns (1993) (0)
Some properties of the dynamics of two interacting particles in a uniform magnetic field (2007) (0)
Phase Diagrams of Majority Voter Probabilistic Cellular Automata (2015) (0)
Chaos in Systems with Noise (0)
Reasons to use maths (1997) (0)
HERMITE-HADAMARD INEQUALITY FOR COORDINATED Fh-CONVEX FUNCTIONS ON TIME SCALES (2021) (0)
Modulation Including Blocking Oscillation (1993) (0)
Chaotic Evolution and Strange Attractors: The Statistical Analysis of Time Series for Deterministic Nonlinear Systems (David Ruelle) (1991) (0)
Multichannel Transmission and Fetal Studies (1993) (0)
Collapse of Tori and Genesis of Chaos in Dissipative Systems (1987) (0)
Numerical simulation fo continuous systems (2013) (0)
Marine bioacoustics: by William N. Tavolga (Ed.), Pergamon (1964) (1966) (0)
Appendix 2. Frequency Choice (1993) (0)
Renormalisation for invariant circles (1993) (0)
Pressure Sensing and Transmission (1993) (0)
Sensors and Transmitters for Other Variables (1993) (0)
Receivers and Demodulators (1993) (0)
STATIONARY STATES OF COUPLED BISTABLE ELEMENTS (1995) (0)
Short communication On generation-integrated energy storage (2015) (0)
Inward Power and Telestimulation (1993) (0)
An Overview of the Behaviour of a Scattering Map for the Dynamics of Two Interacting Particles in a Uniform Magnetic Field (2011) (0)
Erratum to “Discommensuration theory and shadowing in Frenkel–Kontorova models” by C. Baesens and R.S. MacKay [Physica D 216 (2006) 179–184] (2007) (0)
RENORMALIZATION METHODS: CRITICAL PHENOMENA, CHAOS, FRACTAL STRUCTURES By A NNICK L ESNE (translated by L EILA S CHNEPS ): 360 pp., £70.00, ISBN 0 471 96689 4 (John Wiley & Sons, 1998). (2000) (0)
Appendix 6. Stable TemperatureCompensated Oscillator (1993) (0)
Self-organisations and emergence (2013) (0)
Challenges in complex systems science (2012) (0)
Interacting stochastic particle systems (2013) (0)
Appendix 3. Legal Factors (1993) (0)
Proceedings of the workshop on Localization in nonlinear lattices (1998) (0)
Bioelectric and Chemical Electrode Potentials (1993) (0)
Peaceful Picketing and the Criminal Code (1963) (0)
Hyperbolic Structure in Classical Chaos (1993) (0)
Existence and Stability of 3-site Breathers in a Triangular Lattice 2 1 (2004) (0)

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