(See also arxiv and ORCID.)

Papers/Preprints

Multivariate extreme values for dynamical systems (with R. Aimino, A.C. Freitas and J.M. Freitas). Preprint Sept 2024. Countable Markov shifts with exponential mixing (with B. Zhao). Preprint Mar 2024. On distributional limit laws for recurrence (with M. Holland). Preprint Jan 2024. Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems (with A.C. Freitas, J.M. Freitas and I. Melbourne). Electron. J. Probab. 29 (2024) paper no. 170. A trichotomy for hitting times and escape rates for a class of unimodal maps (with M. Demers). Preprint Sept 2023. Hölder continuity of measures for heavy tail potentials (with G. Iommi and D. Terhesiu). Preprint Sept 2024. Orbits closeness for slowly mixing dynamical systems (with J. Rousseau). Ergodic Theory Dynam. Systems 44 (2024) 1192-1208 Cover times in dynamical systems (with N. Jurga). To appear in Israel J. Math. Enriched functional limit theorems for dynamical systems (with A.C. Freitas and J.M. Freitas). Preprint version Jan 2024. Differentiability of the pressure in non-compact spaces (with G. Iommi). Fund. Math. 259 (2022) 151-177. Escape of entropy for countable Markov shifts (with G. Iommi and A. Velozo). Adv. Math. 405 (2022) Paper No. 108507. Asymptotic escape rates and limiting distributions for multimodal maps (with M. Demers). Ergodic Theory Dynam. Systems 41 (2021) 1656-1705. Pressure function and limit theorems for almost Anosov flows (with H. Bruin and D. Terhesiu). Comm. Math. Phys. 382 (2021) 1–47. Upper semi-continuity of entropy in non-compact settings (with G. Iommi and A. Velozo). Math. Res. Lett. 27 (2020) 1055-1077. The pressure function for infinite equilibrium measures (with H. Bruin and D. Terhesiu). Israel J. Math. 32 (2019) 775-826. Hitting and escaping statistics: mixing, targets and holes (with H. Bruin and M. Demers). Adv. Math. 328 (2018) 1263-1298. Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems (with M. Holland). Ergodic Theory Dynam. Systems 39 (2019) 980-1001. Slow and fast escape for open intermittent maps (with M. Demers). Comm. Math. Phys. 351 (2017) 775-835. Free energy and equilibrium states for families of interval maps (with N. Dobbs). Mem. Amer. Math. Soc. 286, Number 1417 (2023) (Note this article was formerly known as `Free Energy Jumps Up'.) Quantifying inhomogeneity in fractal sets (with J.M. Fraser). Nonlinearity 31 (2018) 1313-1330. Return times at periodic points in random dynamics (with N. Haydn). Nonlinearity 30 (2017) 73-89. Linear response for intermittent maps (with V. Baladi). Comm. Math. Phys. 347 (2016) 857-874. Hitting times and periodicity in random dynamics (with J. Rousseau). J. Stat. Phys. 161 (2015) 131-150. Rare Events for the Manneville-Pomeau map (with A.C. Freitas, J.M. Freitas and S. Vaienti). Stoch. Proc. App. 126 (2016) 3463-3479. Equilibrium states, pressure and escape for multimodal maps with holes (with M. Demers). Israel J. Math. 221 (2017) 367-424. Speed of convergence for laws of rare events and escape rates (with A.C. Freitas and J.M. Freitas). Stoch. Proc. App. 125 (2015) 1653-1687. Recurrence statistics for the space of Interval Exchange maps and the Teichmueller flow on the space of translation surfaces (with R. Aimino and M. Nicol). Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 1371-1401. Transience and multifractal analysis (with G. Iommi and T. Jordan). Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017) 407-421. Wild attractors and thermodynamic formalism (with H. Bruin). Monatsh. Math. 178 (2015) 39-83. Recurrence and transience for suspension flows (with G. Iommi and T. Jordan). Israel J. Math. 209 (2015) 547-592. Thermodynamic formalism for interval maps: inducing schemes (with G. Iommi). Dyn. Sys. 28 (2013) 354-380. The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics (with A.C. Freitas and J.M. Freitas). Comm. Math. Phys. 321 (2013) 483-527. Transience and thermodynamic formalism for infinitely branched interval maps (with H. Bruin). J. London Math. Soc. 86 (2012) 171-194. Transience in dynamical systems (with G. Iommi). Ergodic Theory Dynam. Systems 33 (2013) 1450-1476. Extremal index, hitting time statistics and periodicity (with A.C. Freitas and J.M. Freitas). Adv. Math. 231 (2012) 2626-2665. Dimension Theory for Multimodal Maps (with G. Iommi). Ann. Henri Poincaré 12 (2011) 591-620. Extreme Value Laws in dynamical systems for non-smooth observations (with A.C. Freitas and J.M. Freitas). J. Stat. Phys. 142 (2011) 108-126. Natural equilibrium states for multimodal maps (with G. Iommi). Comm. Math. Phys. 300 (2010) 65-94. Multifractal analysis for multimodal maps. Preprint version June 2010. Thermodyamic Formalism for Contracting Lorenz Flows (with M.J. Pacifico). J. Stat. Phys. 139 (2010) 159-176. Hitting Time Statistics and Extreme Value Theory (with A.C. Freitas and J.M. Freitas). Probab. Theory Related Fields 147 (2010) 675-710. Return time statistics for measures with positive Lyapunov exponent (with H. Bruin). Stoch. Dyn. 9 (2009) 81-100. Statistical stability of equilibrium states for interval maps (with J.M. Freitas). Nonlinearity 22 (2009) 259-281. Equilibrium states for potentials with supφ-infφ < htop(f) (with H. Bruin). Comm. Math. Phys. 283 (2008) 579-611. (The published version contains an error in the proof of Lemma 4, see erratum.) Equilibrium states for interval maps: the potential -t log|Df| (with H. Bruin). Ann. Sci. École Norm. Sup. (4) 42 (2009) 559-600. Markov extensions and lifting measures for complex polynomials (with H. Bruin). Ergodic Theory Dynam. Systems 27 (2007) 743-768. Distortion bounds for C2+η unimodal maps. Fund. Math. 193 (2007) 37-77. Complex maps without invariant densities (with H. Bruin). Nonlinearity 19 (2006) 2929-2945. Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles (with J. Llibre). J. Difference Equ. Appl. 12 (2005) 1049-1069. Periods for holomorphic maps via Lefschetz numbers (with J. Llibre). Abstr. Appl. Anal. 2005 575-580. Real Ck Koebe Principle (with W. Shen). Fund. Math. 185 (2005) 61-69.

Book

• Extremes and Recurrence in Dynamical Systems (with V. Lucarini, D. Faranda, A.C. Freitas, J.M. Freitas, M. Holland, T. Kuna, M. Nicol, S. Vaienti). Pure and Applied Mathematics: A Wiley Series of Texts, Monographs, and Tracts, 2016, pp312.

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m.todd - at - st-andrews.ac.uk