2026 Ian Melbourne: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	46	1369	1176	99	86	157	7908

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

1369

1176

157

7908

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

758
Citations
On the Implementation of the 0-1 Test for Chaos

Georg A. Gottwald;Ian Melbourne

539
Citations
A New Test for Chaos

Georg A. Gottwald;Ian Melbourne

510
Citations
Testing for Chaos in Deterministic Systems with Noise

Georg A. Gottwald;Ian Melbourne

384
Citations
Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

Ian Melbourne;Matthew Nicol

230
Citations
Large deviations for nonuniformly hyperbolic systems

Ian Melbourne;Matthew Nicol

196
Citations
On the validity of the 0-1 test for chaos

Georg A Gottwald;Ian Melbourne

191
Citations
The 0-1 Test for Chaos: A Review

Georg A. Gottwald;Ian Melbourne

168
Citations
Application of the 0-1 test for chaos to experimental data

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

153
Citations
Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry

I. Melbourne;P. Chossat;M. Golubitsky

151
Citations
The Lorenz Attractor is Mixing

Stefano Luzzatto;Ian Melbourne;Frederic Paccaut

142
Citations
Steady-State bifurcation with 0(3)-Symmetry

Pascal Chossat;Reiner Lauterbach;Ian Melbourne

139
Citations
Asymptotic stability of heteroclinic cycles in systems with symmetry. II

Martin Krupa;Ian Melbourne

131
Citations
A vector-valued almost sure invariance principle for hyperbolic dynamical systems

Ian Melbourne;Matthew Nicol

130
Citations
Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows

Ian Melbourne

122
Citations
An example of a nonasymptotically stable attractor

I Melbourne

119
Citations
Smooth approximation of stochastic differential equations

David Kelly;Ian Melbourne

114
Citations
Statistical limit theorems for suspension flows

Ian Melbourne;Andrei Török;Andrei Török

111
Citations
Large and moderate deviations for slowly mixing dynamical systems

Ian Melbourne

107
Citations
Homogenization for Deterministic Maps and Multiplicative Noise

Georg A. Gottwald;Ian Melbourne

102
Citations
The Structure of Symmetric Attractors

Ian Melbourne;Michael Dellnitz;Martin Golubitsky

98
Citations
An example of a non-asymptotically stable attractor

I. Melbourne

94
Citations

Frequent Co-Authors

Michael Dellnitz University of Paderborn

Martin Golubitsky The Ohio State University

Peter Ashwin University of Exeter

Andrew M. Stuart California Institute of Technology

Jerrold E. Marsden California Institute of Technology

Guido Schneider University of Stuttgart

Peter K. Friz Technical University of Berlin

Arnd Scheel University of Minnesota

External Links

Personal website of Ian Melbourne Google Scholar page

If you think any of the details on this page are incorrect, let us know.

Related Online Degrees & Career Pathways

For students interested in expanding their skill set beyond Mathematics, pursuing related business degrees online offers flexible and practical options. Programs such as the easy online MBA allow individuals to gain essential management knowledge without overwhelming coursework, making it accessible for those balancing work and study.

If accreditation and budget are key concerns, exploring the cheapest AACSB online DBA options can provide high-quality education with recognized credentials, helping graduates advance into leadership and research roles with confidence.

Similarly, those interested in finance-related careers may consider an affordable pathway like the cheap online masters in finance. This degree complements mathematical expertise with financial theory and practice, opening doors to careers in banking, investment, and risk analysis.

For students eager to finish quickly, accelerated MBA programs online offer condensed timelines that help launch business careers sooner, fitting well with the drive and discipline often found in Mathematics graduates.