Ian Melbourne
Impact in
- Statistical and Nonlinear Physics top 0.2%
- Chaos control and synchronization
- Quantum chaos and dynamical systems
- stochastic dynamics and bifurcation
- Mathematical Physics top 0.5%
- Mathematical Dynamics and Fractals
- Stochastic processes and statistical mechanics
Papers in
-
- Quantum chaos and dynamical systems 59
- Chaos control and synchronization 20
-
- Mathematical Dynamics and Fractals 71
- Stochastic processes and statistical mechanics 18
- advanced mathematical theories 8
- Co-authors
- Georg A. Gottwald (13 shared papers)Matthew Nicol (13 shared papers)Martin Krupa (3 shared papers)Martin Golubitsky (5 shared papers)Andrei Török (10 shared papers)Pascal Chossat (4 shared papers)Peter Ashwin (6 shared papers)Michael Dellnitz (7 shared papers)
- Journals
- Nonlinearity (16 papers)Ergodic Theory and Dynamical Systems (12 papers)Transactions of the American Mathematical Society (5 papers)Archive for Rational Mechanics and Analysis (5 papers)Annales de l Institut Henri Poincaré Probabilités et Statistiques (4 papers)
- Partner nations
- United KingdomUnited StatesGermany
In The Last Decade
Ian Melbourne
109 papers receiving 3.5k citations
Ian Melbourne's Hit Papers
Peers
Comparison fields: 5 of 98
- Statistical and Nonlinear Physics 2.1k
- Mathematical Physics 1.1k
- Geometry and Topology 479
- Computer Networks and Communications 1.2k
- Modeling and Simulation 162
Countries citing papers authored by Ian Melbourne
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
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-authors
The 25 scholars most cited alongside Ian Melbourne, linked wherever they have co-authored with each other. Click a name or a connecting line to browse the papers they share.
All Works
Showing the 20 most-cited of 113 papers — load more, or switch the sort, to bring in the rest.
| # | Work | ||
|---|---|---|---|
| 1 | A new test for chaos in deterministic systems Hit paper breakdown → | 2004 | 510 |
| 2 | On the Implementation of the 0–1 Test for Chaos Hit paper breakdown → | 2009 | 383 |
| 3 | 2005 | 241 | |
| 4 | 2009 | 145 | |
| 5 | 1995 | 137 | |
| 6 | 2016 | 122 | |
| 7 | 2007 | 98 | |
| 8 | 2005 | 97 | |
| 9 | 1989 | 87 | |
| 10 | 2008 | 82 | |
| 11 | 1991 | 76 | |
| 12 | 2016 | 64 | |
| 13 | 2004 | 63 | |
| 14 | 1993 | 60 | |
| 15 | 1991 | 59 | |
| 16 | 2004 | 54 | |
| 17 | 2009 | 53 | |
| 18 | 2008 | 51 | |
| 19 | 1997 | 50 | |
| 20 | 1992 | 46 |
About Ian Melbourne
Ian Melbourne is a scholar working on Statistical and Nonlinear Physics, Mathematical Physics, Computer Networks and Communications, Geometry and Topology and Finance, having authored 113 papers that have together received 3.7k indexed citations. Recurring topics across this work include Mathematical Dynamics and Fractals (71 papers), Quantum chaos and dynamical systems (59 papers), Nonlinear Dynamics and Pattern Formation (40 papers), Chaos control and synchronization (20 papers), Advanced Differential Equations and Dynamical Systems (20 papers), Stochastic processes and statistical mechanics (18 papers), Stochastic processes and financial applications (8 papers) and advanced mathematical theories (8 papers). The work is most often cited by research in Statistical and Nonlinear Physics (2.1k citations), Mathematical Physics (1.1k citations), Geometry and Topology (479 citations), Computer Networks and Communications (1.2k citations) and Modeling and Simulation (162 citations). Ian Melbourne has collaborated with scholars based in United Kingdom, United States and Germany. Frequent co-authors include Georg A. Gottwald, Matthew Nicol, Martin Krupa, Martin Golubitsky, Andrei Török, Pascal Chossat, Peter Ashwin, Michael Dellnitz, David Kelly and Michael Field. Their work appears in journals such as Nonlinearity, Ergodic Theory and Dynamical Systems, Transactions of the American Mathematical Society, Archive for Rational Mechanics and Analysis and Annales de l Institut Henri Poincaré Probabilités et Statistiques.
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.