Ian Melbourne's Publication List

Publications on the Lorenz attractor

1. W. Bahsoun, I. Melbourne and M. Ruziboev. Variance continuity for Lorenz flows.
   Annales Henri Poincaré 21 (2020) 1873-1892. (abstract, pdf file, published version)

2. V. Araújo and I. Melbourne. Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation.
   Adv. Math. 349 (2019) 212-245. (abstract, pdf file)

3. P. Bálint and I. Melbourne. Statistical properties for flows with unbounded roof function, including the Lorenz attractor.
   J. Stat. Phys. 172 (2018) 1101-1126. (abstract, pdf file, View only of published version)
   

4. V. Araújo and I. Melbourne. Existence and smoothness of the stable foliation for sectional hyperbolic attractors.
   Bull. London Math. Soc. 49 (2017) 351-367. (abstract, pdf file)

5. V. Araújo and I. Melbourne. Exponential decay of correlations for nonuniformly hyperbolic flows with a C^1+α stable foliation, including the classical Lorenz attractor.
   Annales Henri Poincaré. 17 (2016) 2975-3004. (abstract, pdf file, View only of published version)

6. V. Araújo, I. Melbourne and P. Varandas. Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps.
   Commun. Math. Phys. 340 (2015) 901-938. (abstract, pdf file)

7. M. Holland and I. Melbourne. Central limit theorems and invariance principles for Lorenz attractors.
   J London Math Soc 76 (2007) 345-364. (abstract, pdf file)

8. S. Luzzatto, I. Melbourne and F. Paccaut. The Lorenz attractor is mixing.
   Commun. Math. Phys. 260 (2005) 393-401. (abstract, pdf file)