Ian Melbourne's Publication List

Publications on infinite measure systems

1. D. Coates, I. Melbourne and A. Talebi. Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points.
   Preprint, July 2024. (abstract, pdf file)

2. P. Eslami, I. Melbourne and S. Vaienti. Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps.
   Adv. Math. 388 (2021) 107853. (abstract, pdf file)

3. I. Melbourne and D. Terhesiu. Renewal theorems and mixing for non Markov flows with infinite measure.
   Ann. Inst. H. Poincaré (B) Probab. Statist. 56 (2020) 449-476. (abstract, pdf file, published version)

4. H. Bruin, I. Melbourne and D. Terhesiu. Rates of mixing for nonMarkov infinite measure semiflows.
   Trans. Amer. Math. Soc. 371 (2019) 7343-7386. (abstract, pdf file)

5. I. Melbourne and D. Terhesiu. Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure.
   J. Mod. Dyn. 12 (2018) 285-313. (abstract, pdf file)

6. I. Melbourne and D. Terhesiu. Operator renewal theory for continuous time dynamical systems with finite and infinite measure.
   Monatsh. Math. 182 (2017) 377-431. (abstract, pdf file, View only of published version)

7. I. Melbourne. Mixing for invertible dynamical systems with infinite measure.
   Stoch. Dyn. 15 (2015) 1550012 (25 pages). (abstract, pdf file)

8. I. Melbourne and D. Terhesiu. First and higher order uniform dual ergodic theorems for dynamical systems with infinite measure.
   Israel J. Math. 194 (2013) 793-830. (abstract, pdf file)

9. I. Melbourne and D. Terhesiu. Operator renewal theory and mixing rates for dynamical systems with infinite measure.
   Inventiones Mathematicae 189 (2012) 61-110 (abstract, pdf file, corrected version, March 2015)