Ian Melbourne

5.8k total citations · 2 hit papers
106 papers, 3.3k citations indexed

About

Ian Melbourne is a scholar working on Mathematical Physics, Statistical and Nonlinear Physics and Computer Networks and Communications. According to data from OpenAlex, Ian Melbourne has authored 106 papers receiving a total of 3.3k indexed citations (citations by other indexed papers that have themselves been cited), including 70 papers in Mathematical Physics, 70 papers in Statistical and Nonlinear Physics and 37 papers in Computer Networks and Communications. Recurrent topics in Ian Melbourne's work include Mathematical Dynamics and Fractals (70 papers), Quantum chaos and dynamical systems (54 papers) and Nonlinear Dynamics and Pattern Formation (37 papers). Ian Melbourne is often cited by papers focused on Mathematical Dynamics and Fractals (70 papers), Quantum chaos and dynamical systems (54 papers) and Nonlinear Dynamics and Pattern Formation (37 papers). Ian Melbourne collaborates with scholars based in United Kingdom, United States and Australia. Ian Melbourne's co-authors include Georg A. Gottwald, Matthew Nicol, Martin Krupa, Martin Golubitsky, Andrei Török, Pascal Chossat, Peter Ashwin, David Kelly, Michael Dellnitz and Michael Field and has published in prestigious journals such as Proceedings of the National Academy of Sciences, Communications in Mathematical Physics and Annals of Mathematics.

In The Last Decade

Ian Melbourne

103 papers receiving 3.1k citations

Hit Papers

A new test for chaos in deterministic systems 2004 2026 2011 2018 2004 2009 100 200 300 400
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. A new test for chaos in deterministic systems
    2004 464 citations Georg A. Gottwald, Ian Melbourne profile →
  2. On the Implementation of the 0–1 Test for Chaos
    2009 366 citations Georg A. Gottwald, Ian Melbourne profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Ian Melbourne United Kingdom 30 1.9k 1.1k 1.0k 410 382 106 3.3k
Georg A. Gottwald Australia 25 2.1k 1.1× 650 0.6× 566 0.5× 199 0.5× 406 1.1× 98 3.4k
Jean-Marie Strelcyn France 17 3.1k 1.6× 1.3k 1.2× 615 0.6× 416 1.0× 301 0.8× 30 4.0k
Mitchell J. Feigenbaum United States 17 3.5k 1.9× 2.2k 2.0× 1.2k 1.1× 382 0.9× 607 1.6× 30 5.2k
Tien-Yien Li United States 9 1.1k 0.6× 503 0.5× 890 0.9× 391 1.0× 349 0.9× 15 2.4k
D.S. Mazel United States 7 1.4k 0.7× 917 0.9× 382 0.4× 339 0.8× 144 0.4× 20 3.1k
Andrzej Lasota Poland 24 1.2k 0.7× 390 0.4× 1.1k 1.0× 276 0.7× 189 0.5× 97 3.3k
Antonio Giorgilli Italy 29 3.4k 1.8× 1.2k 1.1× 469 0.5× 201 0.5× 230 0.6× 92 4.5k
Helena E. Nusse United States 23 1.8k 0.9× 862 0.8× 512 0.5× 493 1.2× 359 0.9× 50 2.6k
Irene M. Moroz United Kingdom 27 1.3k 0.7× 803 0.8× 329 0.3× 132 0.3× 105 0.3× 151 2.9k
J. C. Alexander United States 28 1.2k 0.6× 863 0.8× 588 0.6× 225 0.5× 72 0.2× 89 2.9k

Countries citing papers authored by Ian Melbourne

Since Specialization
Citations

This map shows the geographic impact of Ian Melbourne's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Ian Melbourne with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Ian Melbourne more than expected).

Fields of papers citing papers by Ian Melbourne

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Ian Melbourne. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Ian Melbourne. The network helps show where Ian Melbourne may publish in the future.

Co-authorship network of co-authors of Ian Melbourne

This figure shows the co-authorship network connecting the top 25 collaborators of Ian Melbourne. A scholar is included among the top collaborators of Ian Melbourne based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Ian Melbourne. Ian Melbourne is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Gottwald, Georg A. & Ian Melbourne. (2024). Time-reversibility and nonvanishing Lévy area. Nonlinearity. 37(7). 75018–75018.
2.
Matheus, Carlos, et al.. (2024). Polynomial decay of correlations for nonpositively curved surfaces. Transactions of the American Mathematical Society. 377(9). 6043–6095. 1 indexed citations
3.
Melbourne, Ian, et al.. (2023). Local large deviations for periodic infinite horizon Lorentz gases. Journal d Analyse Mathématique. 152(1). 283–316. 1 indexed citations
4.
Melbourne, Ian, et al.. (2019). Sharp Statistical Properties for a Family of Multidimensional\n NonMarkovian Nonconformal Intermittent Maps. arXiv (Cornell University). 1 indexed citations
5.
Melbourne, Ian, et al.. (2018). Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure \n. Warwick Research Archive Portal (University of Warwick). 1 indexed citations
6.
Kelly, David & Ian Melbourne. (2017). Deterministic homogenization for fast–slow systems with chaotic noise. Journal of Functional Analysis. 272(10). 4063–4102. 39 indexed citations
7.
Melbourne, Ian, et al.. (2017). Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems. Studia Mathematica. 238(1). 59–89. 4 indexed citations
8.
Gottwald, Georg A. & Ian Melbourne. (2016). On the detection of superdiffusive behaviour in time series \n. Warwick Research Archive Portal (University of Warwick). 3 indexed citations
9.
Melbourne, Ian, et al.. (2016). Operator renewal theory for continuous time dynamical systems with finite and infinite measure. Monatshefte für Mathematik. 182(2). 377–431. 8 indexed citations
10.
Melbourne, Ian. (2008). Large and moderate deviations for slowly mixing dynamical systems. Proceedings of the American Mathematical Society. 137(5). 1735–1741. 48 indexed citations
11.
Lamb, Jeroen S. W. & Ian Melbourne. (2007). Normal form theory for relative equilibria and relative periodic solutions. Transactions of the American Mathematical Society. 359(9). 4537–4557. 3 indexed citations
12.
Melbourne, Ian & Guido Schneider. (2004). Phase dynamics in the complex Ginzburg–Landau equation. Journal of Differential Equations. 199(1). 22–46. 14 indexed citations
13.
Lamb, Jeroen S. W., Ian Melbourne, & Claudia Wulff. (2003). Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions. Journal of Differential Equations. 191(2). 377–407. 15 indexed citations
14.
Melbourne, Ian, et al.. (1999). Bifurcation from Discrete Rotating Waves. Archive for Rational Mechanics and Analysis. 149(3). 229–270. 24 indexed citations
15.
Chossat, Pascal, Martin Krupa, Ian Melbourne, & Arnd Scheel. (1997). Transverse bifurcations of homoclinic cycles. Physica D Nonlinear Phenomena. 100(1-2). 85–100. 23 indexed citations
16.
Dellnitz, Michael & Ian Melbourne. (1994). Generic movement of eigenvalues for equivariant self-adjoint matrices. Journal of Computational and Applied Mathematics. 55(3). 249–259. 7 indexed citations
17.
Melbourne, Ian, Michael Dellnitz, & Martin Golubitsky. (1993). The structure of symmetric attractors. Archive for Rational Mechanics and Analysis. 123(1). 75–98. 47 indexed citations
18.
Chossat, Pascal, Reiner Lauterbach, & Ian Melbourne. (1991). Steady-State bifurcation with 0(3)-Symmetry. Archive for Rational Mechanics and Analysis. 113(4). 313–376. 60 indexed citations
19.
Melbourne, Ian. (1991). An example of a nonasymptotically stable attractor. Nonlinearity. 4(3). 835–844. 53 indexed citations
20.
Melbourne, Ian. (1986). A singularity theory analysis of bifurcation problems with octahedral symmetry. Dynamics and Stability of Systems. 1(4). 293–321. 13 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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