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D-Index & Metrics

Mathematics

D-Index
46
Citations
7908
World Ranking
1369
National Ranking
99

Ian Melbourne publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Ian Melbourne sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 157 publications — 42nd percentile

42% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Ian Melbourne D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Ian Melbourne sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 46 D-Index — 64th percentile

64% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Overview

Ian Melbourne is a researcher affiliated with the University of Warwick in the United Kingdom. Their academic work is principally within the field of Mathematics, with a particular focus on Mathematical Physics, encompassing subfields such as Statistical and Nonlinear Physics, Finance, Computational Theory and Mathematics, and Applied Mathematics.

The research topics covered by Melbourne include:

  • Mathematical Dynamics and Fractals
  • Stochastic processes and statistical mechanics
  • Stochastic processes and financial applications
  • Advanced mathematical theories
  • Quantum chaos and dynamical systems
  • Advanced Mathematical Modeling in Engineering
  • Nonlinear Dynamics and Pattern Formation

Melbourne's publication record includes numerous papers across various respected venues with a presence in journals and preprint servers including arXiv, Electronic Journal of Probability, and the Annales de l'Institut Henri Poincaré Probabilités et Statistiques. Frequent publication outlets also include Probability Theory and Related Fields and Annales Henri Poincaré.

Key recent publications are as follows:

  • Superdiffusive limits for deterministic fast-slow dynamical systems, 2020, Probability Theory and Related Fields
  • Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems, 2022, Electronic Journal of Probability
  • Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1, 2022, Annales de l'Institut Henri Poincaré Probabilités et Statistiques
  • Simulation of Non-Lipschitz Stochastic Differential Equations Driven by α-Stable Noise: A Method Based on Deterministic Homogenization, 2021, Multiscale Modeling and Simulation
  • Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2, 2022, Annales de l'Institut Henri Poincaré Probabilités et Statistiques

The scientist collaborates regularly with a group of coauthors, including:

  • Dalia Terhesiu
  • Alexey Korepanov
  • Ilya Chevyrev
  • Georg A. Gottwald
  • Nicolò Paviato

Melbourne's contributions reflect a strong emphasis on advanced mathematical modeling and analytical techniques related to deterministic and stochastic dynamical systems. The research integrates rigorous probabilistic approaches to problems in dynamics and stochastic analysis, addressing themes such as homogenization and large deviations in complex mathematical frameworks.

Best Publications

  • A new test for chaos in deterministic systems

    Georg A. Gottwald;Ian Melbourne

  • On the Implementation of the 0-1 Test for Chaos

    Georg A. Gottwald;Ian Melbourne

  • A New Test for Chaos

    Georg A. Gottwald;Ian Melbourne

  • Testing for Chaos in Deterministic Systems with Noise

    Georg A. Gottwald;Ian Melbourne

  • Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

    Ian Melbourne;Matthew Nicol

  • Large deviations for nonuniformly hyperbolic systems

    Ian Melbourne;Matthew Nicol

  • On the validity of the 0-1 test for chaos

    Georg A Gottwald;Ian Melbourne

  • The 0-1 Test for Chaos: A Review

    Georg A. Gottwald;Ian Melbourne

  • Application of the 0-1 test for chaos to experimental data

    Ian Falconer;Georg A. Gottwald;Ian Melbourne;Kjetil Wormnes

  • Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry

    I. Melbourne;P. Chossat;M. Golubitsky

  • The Lorenz Attractor is Mixing

    Stefano Luzzatto;Ian Melbourne;Frederic Paccaut

  • Steady-State bifurcation with 0(3)-Symmetry

    Pascal Chossat;Reiner Lauterbach;Ian Melbourne

  • Asymptotic stability of heteroclinic cycles in systems with symmetry. II

    Martin Krupa;Ian Melbourne

  • A vector-valued almost sure invariance principle for hyperbolic dynamical systems

    Ian Melbourne;Matthew Nicol

  • Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows

    Ian Melbourne

  • An example of a nonasymptotically stable attractor

    I Melbourne

  • Smooth approximation of stochastic differential equations

    David Kelly;Ian Melbourne

  • Statistical limit theorems for suspension flows

    Ian Melbourne;Andrei Török;Andrei Török

  • Large and moderate deviations for slowly mixing dynamical systems

    Ian Melbourne

  • Homogenization for Deterministic Maps and Multiplicative Noise

    Georg A. Gottwald;Ian Melbourne

  • The Structure of Symmetric Attractors

    Ian Melbourne;Michael Dellnitz;Martin Golubitsky

  • An example of a non-asymptotically stable attractor

    I. Melbourne

Frequent Co-Authors

Michael Dellnitz
Michael Dellnitz University of Paderborn
Martin Golubitsky
Martin Golubitsky The Ohio State University
Peter Ashwin
Peter Ashwin University of Exeter
Andrew M. Stuart
Andrew M. Stuart California Institute of Technology
Jerrold E. Marsden
Jerrold E. Marsden California Institute of Technology
Guido Schneider
Guido Schneider University of Stuttgart
Peter K. Friz
Peter K. Friz Technical University of Berlin
Arnd Scheel
Arnd Scheel University of Minnesota
Michael R. E. Proctor
Michael R. E. Proctor University of Cambridge

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