Ian Melbourne's Publication List

Publications on Mixing Rates for Flows

1. Y. Lima, C. Matheus and I. Melbourne. Polynomial decay of correlations for nonpositively curved surfaces.
   Trans. Amer. Math. Soc. 377 (2024) 6043-6095. (abstract, pdf file)

2. I. Melbourne and P. Varandas. Good inducing schemes for uniformly hyperbolic flows, and applications to exponential decay of correlations.
   Ann. Henri Poincaré 26 (2025) 921-945. (abstract, pdf file, link to journal version)

3. I. Melbourne, N. Paviato and D. Terhesiu. Decay in norm of transfer operators for semiflows.
   Studia Math. 266 (2022) 149-166. (abstract, pdf file, OnlineFirst version)

4. I. Melbourne, N. Paviato and D. Terhesiu. Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems.
   Israel. J. Math. 247 (2022) 987-991. (abstract, pdf file, View only of published version)

5. P. Bálint, O. Butterley and I. Melbourne. Polynomial decay of correlations for flows, including Lorentz gas examples.
   Commun. Math. Phys. 368 (2019) 55-111. (abstract, pdf file, View only of published version)

6. 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)

7. I. Melbourne. Superpolynomial and polynomial mixing for semiflows and flows.
   Nonlinearity 31 (2018) R268-R316. (abstract, pdf file)

8. 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)

9. 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)

10. I. Melbourne. Decay of correlations for slowly mixing flows.
    Proc. London Math. Soc. 98 (2009) 163-190. (abstract, pdf file)

11. P. Bálint and I. Melbourne. Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows.
    J. Stat. Phys. 133 (2008) 435-447. (abstract, pdf file)

12. M. Field, I. Melbourne and A. Török. Stability of mixing and rapid mixing for hyperbolic flows.
    Annals of Mathematics 166 (2007) 269-291. (abstract, pdf file)

13. I. Melbourne. Rapid decay of correlations for nonuniformly hyperbolic flows.
    Trans. Amer. Math. Soc. 359 (2007) 2421-2441. (abstract, pdf file)