Ian Melbourne's Reprint List

Ergodic Theory

1. I. Melbourne and D. Terhesiu. Mixing for continuous time dynamical systems with infinite measure. Preprint. July 2013.
   ( abstract, postscript file or pdf file )

2. I. Melbourne and R. Zweimüller. Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems. Preprint. January 2013. Final version September 2013. To appear in Ann. Inst. H. Poincaré Probab. Statist.
   ( abstract, postscript file or pdf file )

3. G. Gottwald and I. Melbourne. Central limit theorems and suppression of anomalous diffusion for systems with s ymmetry. Preprint, November 2012.
   ( abstract, postscript file or pdf file )

4. I. Melbourne. Mixing for invertible infinite measure systems. Preprint, November 2012.
   ( abstract, postscript file or pdf file )

5. G. Gottwald and I. Melbourne. A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proc. Natl. Acad. Sci. USA 110 (2013) 8411-8416.
   ( abstract, postscript file or pdf file )

6. S. Luzzatto and I. Melbourne. Statistical properties and decay of correlations for interval maps with critical points and singularities. Commun. Math. Phys. 320 (2013) 21-35.
   ( abstract, postscript file or pdf file )

7. 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, postscript file or pdf file )

8. I. Melbourne and D. Terhesiu. Decay of correlations for nonuniformly expanding systems with general return times. Preprint, May 2011. Updated August 2011. To appear in Ergodic Theory Dyn. Syst.
   ( abstract, postscript file or pdf file )

9. P. Bálint and I. Melbourne. Decay of correlations for flows with unbounded roof function, including the infinite horizon planar periodic Lorentz gas. Preprint, November 2010.
   ( abstract, postscript file or pdf file )

10. I. Melbourne and A. Török. Convergence of moments for Axiom A and nonuniformly hyperbolic flows. Ergodic Theory Dyn. Syst. 32 (2012) 1091-1100
    ( abstract, postscript file or pdf file )

11. I. Melbourne and D. Terhesiu. Operator renewal theory and mixing rates for dynamical systems with infinite measure. Inventiones Mathematicae 189 (2012) 61-110
    ( abstract, postscript file or pdf file )

12. I. Melbourne, V. Niţică and A. Török. Transitivity of Heisenberg group extensions of hyperbolic systems. Ergodic Theory Dyn. Syst. 32 (2012) 223-235
    ( abstract, postscript file or pdf file )

13. H. Bruin, M. Demers and I. Melbourne. Existence and convergence properties of physical measures for certain dynamical systems with holes.
    Ergodic Theory Dyn. Syst. 30 (2010) 687-728.
    ( abstract, postscript file or pdf file )

14. I. Melbourne, V. Niţică and A. Török. Transitivity of Euclidean-type extensions of hyperbolic systems. Ergodic Theory Dyn. Syst. 29 (2009) 1585-1602.
    ( abstract, postscript file or pdf file )

15. I. Melbourne and M. Nicol. A vector-valued almost sure invariance principle for hyperbolic dynamical systems. Annals of Probability 37 (2009) 478-505.
    ( abstract, postscript file or pdf file )

16. I. Melbourne. Large and moderate deviations for slowly mixing dynamical systems. Proc. Amer. Math. Soc. 137 (2009) 1735-1741.
    ( abstract, postscript file or pdf file )

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

18. 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, postscript file or pdf file )

19. I. Melbourne and M. Nicol. Large deviations for nonuniformly hyperbolic systems. Trans. Amer. Math. Soc. 360 (2008) 6661-6676.
    ( abstract, postscript file or pdf file )

20. I. Melbourne and G. Gottwald. Power spectra for deterministic chaotic dynamical systems. Nonlinearity 21 (2008) 179-189.
    ( abstract, postscript file or pdf file )

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

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

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

24. I. Melbourne, V. Niţică and A. Török. A note about stable transitivity of noncompact extensions of hyperbolic systems. Disc. Cont. Dyn. Syst. 14 (2006) 355-363.
    ( abstract, postscript file or pdf file )

25. I. Melbourne and A. Windsor. A C^∞ diffeomorphism with infinitely many intermingled basins. Ergodic Theory Dyn. Syst. 25 (2005) 1951-1959.
    ( abstract, postscript file or pdf file )

26. H. Bruin, M. Holland and I. Melbourne. Subexponential decay of correlations for compact group extensions of nonuniformly expanding systems. Ergodic Theory Dyn. Syst. 25 (2005) 1719-1738.
    ( abstract, postscript file or pdf file )

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

28. I. Melbourne and M. Nicol. Almost sure invariance principle for nonuniformly hyperbolic systems. Commun. Math. Phys. 260 (2005) 131-146.
    ( abstract, postscript file or pdf file )

29. I. Melbourne, V. Niţică and A. Török. Stable transitivity of certain noncompact extensions of hyperbolic systems. Annales Henri Poincaré 6 (2005) 725-746.
    ( abstract, postscript file or pdf file )

30. M. Field, I. Melbourne and A. Török. Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets. Ergodic Theory Dyn. Syst. 25 (2005) 517-551.
    ( abstract, postscript file or pdf file )

31. M. Field, I. Melbourne, M. Nicol and A. Török. Statistical properties of compact group extensions of hyperbolic flows and their time one maps. Disc. Cont. Dyn. Syst. 12 (2005) 79-96.
    ( abstract, postscript file or pdf file )

32. I. Melbourne and A. Török. Statistical limit theorems for suspension flows. Israel Journal of Math. 144 (2004) 191-209.
    ( abstract, postscript file or pdf file )

33. I. Melbourne and M. Nicol. Statistical properties of endomorphisms and compact group extensions. J. London Math. Soc. 70 (2004) 427-446.
    ( abstract, postscript file or pdf file )

34. I. Melbourne and M. Nicol. Statistical limit laws for equivariant observations. Stochastics and Dynamics 4 (2004) 1-13.
    ( abstract, postscript file or pdf file )

35. M. Ådahl, I. Melbourne and M. Nicol. Random iteration of Euclidean isometries. Nonlinearity 16 (2003) 977-987.
    ( abstract, postscript file or pdf file )

36. M. Field, I. Melbourne and A. Török. Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions. Ergodic Theory Dyn. Syst. 23 (2003) 87-110.
    ( abstract, postscript file or pdf file )

37. I. Melbourne and M. Nicol. Stable transitivity of Euclidean group extensions. Ergodic Theory Dyn. Syst. 23 (2003) 611-619.
    ( abstract, postscript file or pdf file )

38. I. Melbourne and A. Török. Central limit theorems and invariance principles for time-one maps of hyperbolic flows. Commun. Math. Phys. 229 (2002) 57-71.
    ( abstract, postscript file or pdf file )

39. P. Ashwin, I. Melbourne and M. Nicol. Hypermeander of spirals; local bifurcations and statistical properties. Physica D 156 (2001) 364-382.
    ( abstract, postscript file or pdf file )

40. M. Nicol, I. Melbourne and P. Ashwin. Euclidean extensions of dynamical systems. Nonlinearity. 14 (2001) 275-300.
    ( abstract, postscript file or pdf file )

41. P. Ashwin, I. Melbourne and M. Nicol. Drift for Euclidean extensions of dynamical systems. Equadiff 99, International Conference on Differential Equations , (B. Fiedler et al. eds.) World Scientific, Singapore, 2000, 145-150.
    ( abstract, postscript file or pdf file )