Ian Melbourne
Mathematical Physics · 2002–2016
A researcher in the Science corpus: 17 papers; trusts 20 researchers and is trusted by 20 researchers here, as inferred from the citation graph.
Subfields
- Mathematical Physics — 53 citations into it; #1,162 of 8,562 by trust here, #773 by citations
- Statistical and Nonlinear Physics — 24 citations into it; #1,190 of 10,127 by trust here, #1,755 by citations
- Geometry and Topology — 21 citations into it; #6,546 of 7,422 by trust here, #4,709 by citations
- Finance — 13 citations into it; #5,770 of 10,518 by trust here, #5,728 by citations
- Statistics and Probability — 11 citations into it
- Applied Mathematics — 7 citations into it; #6,754 of 7,620 by trust here, #4,749 by citations
- Computational Theory and Mathematics — 5 citations into it
Whom Ian Melbourne trusts overall
Their strongest outbound trust, strongest first, inferred from their citations.
- S. Gouëzel
- O. Sarig
- Dmitry Dolgopyat
- Georg A. Gottwald
- Liverani Carlangelo
- Floris Takens
- Roland Zweimüller
- Huyi Hu
- Maximilian Thaler
- Peter K. Friz
Who trusts Ian Melbourne overall
- Georg A. Gottwald
- A. Korepanov
- Charalampos Skokos
- E. Rio
- Alexander I. Bufetov
- Mark Holland
- David Kelly
- Zemer Kosloff
- Matthew Nicol
- Ale Jan Homburg
Papers from Ian Melbourne's perspective
Ordered by how strongly the researchers Ian Melbourne trusts endorse each paper. Same corpus, a different order for every researcher.
- Sharp polynomial estimates for the decay of correlations
- Limit theorems for partially hyperbolic systems
- On Contact Anosov Flows
- Perturbation theory for linear operators
- Central limit theorem and stable laws for intermittent maps
- Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness
- SRB measures for non-hyperbolic systems with multidimensional expansion
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
- Large deviations for nonuniformly hyperbolic systems
- Averaging and Invariant Measures
Their papers
- Smooth approximation of stochastic differential equations (2014) — 101 citations
- Testing for Chaos in Deterministic Systems with Noise (2004) — 301 citations
- Homogenization for deterministic maps and multiplicative noise (2013) — 89 citations
- On the Implementation of the 0-1 Test for Chaos (2009) — 461 citations
- Martingale–coboundary decomposition for families of dynamical systems (2016) — 48 citations
- Deterministic homogenization for fast–slow systems with chaotic noise (2014) — 84 citations
- Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010) — 88 citations
- On the validity of the 0–1 test for chaos (2009) — 170 citations
- Large deviations for nonuniformly hyperbolic systems (2008) — 171 citations
- Central limit theorems and invariance principles for Lorenz attractors (2007) — 77 citations
- Stability of mixing and rapid mixing for hyperbolic flows (2007) — 79 citations
- Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows (2006) — 71 citations
- Statistical limit theorems for suspension flows (2004) — 107 citations
- The Lorenz Attractor is Mixing (2004) — 133 citations
- Asymptotic stability of heteroclinic cycles in systems with symmetry. II (2004) — 115 citations
- Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions (2003) — 63 citations
- A new test for chaos in deterministic systems (2002) — 623 citations