Difference analogue of the lemma on the logarithmic derivative with applications to difference equations RG Halburd, RJ Korhonen Journal of Mathematical Analysis and Applications 314 (2), 477-487, 2006 | 731 | 2006 |

Nevanlinna theory for the difference operator RG Halburd, RJ Korhonen arXiv preprint math/0506011, 2005 | 568 | 2005 |

Prospects for fundamental physics with LISA E Barausse, E Berti, T Hertog, SA Hughes, P Jetzer, P Pani, TP Sotiriou, ... General Relativity and Gravitation 52, 1-33, 2020 | 388 | 2020 |

On the extension of the Painlevé property to difference equations MJ Ablowitz, R Halburd, B Herbst Nonlinearity 13 (3), 889, 2000 | 299 | 2000 |

Holomorphic curves with shift-invariant hyperplane preimages R Halburd, R Korhonen, K Tohge Transactions of the American Mathematical Society 366 (8), 4267-4298, 2014 | 269 | 2014 |

Finite‐order meromorphic solutions and the discrete Painlevé equations RG Halburd, RJ Korhonen Proceedings of the London Mathematical Society 94 (2), 443-474, 2007 | 235 | 2007 |

Nevanlinna theory for the-difference equations DC Barnett, RG Halburd, W Morgan, RJ Korhonen Proceedings of the Royal Society of Edinburgh Section A: Mathematics 137 (3 …, 2007 | 185 | 2007 |

Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations RG Halburd, RJ Korhonen Journal of Physics A: Mathematical and Theoretical 40 (6), R1, 2007 | 148 | 2007 |

Integrable systems and reductions of the self-dual Yang–Mills equations MJ Ablowitz, S Chakravarty, RG Halburd Journal of Mathematical Physics 44 (8), 3147-3173, 2003 | 109 | 2003 |

Diophantine integrability RG Halburd J. Phys. A: Math. Gen. 38, L263–L269, 2005 | 79 | 2005 |

Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property MD Kruskal, N Joshi, R Halburd Integrability of Nonlinear Systems: Proceedings of the CIMPA School …, 2007 | 71 | 2007 |

Existence of finite-order meromorphic solutions as a detector of integrability in difference equations RG Halburd, RJ Korhonen Physica D: Nonlinear Phenomena 218 (2), 191-203, 2006 | 67 | 2006 |

How to detect the integrability of discrete systems B Grammaticos, RG Halburd, A Ramani, CM Viallet Journal of Physics A: Mathematical and Theoretical 42 (45), 454002, 2009 | 66 | 2009 |

Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem N Joshi, D Burtonclay, RG Halburd letters in mathematical physics 26, 123-131, 1992 | 50 | 1992 |

The generalized Chazy equation from the self‐duality equations MJ Ablowitz, S Chakravarty, R Halburd Studies in Applied Mathematics 103 (1), 75-88, 1999 | 46 | 1999 |

Growth of meromorphic solutions of delay differential equations R Halburd, R Korhonen Proceedings of the American Mathematical Society 145 (6), 2513-2526, 2017 | 45 | 2017 |

Tropical Nevanlinna theory and ultradiscrete equations RG Halburd, NJ Southall International Mathematics Research Notices 2009 (5), 887-911, 2009 | 42 | 2009 |

Movable algebraic singularities of second-order ordinary differential equations G Filipuk, RG Halburd Journal of mathematical physics 50 (2), 2009 | 34 | 2009 |

The generalized Chazy equation and Schwarzian triangle functions MJ Ablowitz, S Chakravarty, R Halburd Asian Journal of Mathematics 2 (4), 619-624, 1998 | 34 | 1998 |

Elementary exact calculations of degree growth and entropy for discrete equations RG Halburd Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2017 | 27 | 2017 |