Ian Melbourne's Preprint List

  1. I. Melbourne, J. Rademacher, B. Rink and S. Zelik. Quasicrystals in pattern formation, Part I: Local existence and basic properties.
    Preprint, October 2024. (abstract, pdf file)

  2. 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)

  3. I. Chevyrev, A. Korepanov and I. Melbourne. Superdiffusive limits beyond the Marcus regime for deterministic fast-slow dynamical systems.
    Preprint, December 2023. To appear in Comm. Amer. Math. Soc. (abstract, pdf file)

  4. A. C. Freitas, J. Freitas, I. Melbourne and M. Todd. Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems.
    Preprint, September 2023. To appear in Electronic. J. Probab. (abstract, pdf file)

  5. V. Biktashev and I. Melbourne. St. Petersburg paradox for quasiperiodically hypermeandering spiral waves.
    Preprint, April 2020. (abstract, pdf file)

  6. P. Ashwin and I. Melbourne. Dynamics on unbounded domains; co-solutions and inheritance of stability.
    Preprint. (abstract, pdf file)


    Pre-preprint

  7. I. Chevyrev, A. Korepanov and I. Melbourne. J1 convergence to Lévy processes for dynamical systems modelled by exponential Young towers.
    September 2023 (abstract, pdf file). This is now subsumed into the beyond Marcus paper (Section 5).