Publications

Ergodic theory of equivariant diffeomorphisms M. Field and M. Nicol. Mem. Amer. Math. Soc. 169 (2004), no. 803, viii+100 pp.

Ergodic Theory: Basic Examples and Constructions M. Nicol and K. Petersen. Encycl. Complex. Syst. Sci.

Springer, New York, 2023, 3–34.

Extremes and Recurrence in Dynamical Systems V. Lucarini, D. Faranda, A. C. M. Freitas, J. M. Freitas, T. Kuna, M. Holland, M. Nicol, M. Todd and S. Vaienti. John Wiley & Sons, Inc., Hoboken, NJ, 2016, xi+295 pp.

Stochastic stability of Bernoulli toral linked twist maps of finite and infinite entropy., M. Nicol. Ergodic Theory Dynam. Systems 16 (1996), no. 3, 493–518.

A Bernoulli toral linked twist map without positive Lyapunov exponents, M. Nicol. Proc. Amer. Math. Soc. 124 (1996), no. 4, 1253–1263.

Induced maps of Bernoulli dynamical systems, M. Nicol. Discrete Contin. Dynam. Systems 7 (2001), no. 1, 147–154.

Measurable cocycle rigidity for some noncompact groups.,  M. Nicol and M. Pollicott. Bull. London Math. Soc. 31 (1999), no. 5, 592–600.

Livsic's Theorem for Semisimple Lie groups.M. Nicol and M. Pollicott. Ergodic Theory Dynam. Systems 21 (2001), no. 5, 1501–1509.

Euclidean extensions of Dynamical Systems., M. Nicol, I. Melbourne and P. Ashwin. Nonlinearity 14 (2001), no. 2, 275–300.

Regularity of invariant graphs over hyperbolic systems., D. Hadjiloucas, M. Nicol and C. Walkden. Ergodic Theory Dynam. Systems 22 (2002), no. 2, 469–482.

On the fine structure of stationary measures in systems which contract-on-average.,  M. Nicol, N. Sidorov and D. Broomhead. J. Theoret. Probab. 15 (2002), no. 3, 715–730.

Stable transitivity of Euclidean group extensions, I. Melbourne and M. Nicol. Ergodic Theory Dynam. Systems 23 (2003), no. 2, 611–619.

Livsic Theorems for  group extensions of hyperbolic systems with  singularities, M. Nicol and A. Scott. Ergodic Theory Dynam. Systems 23 (2003), no. 6, 1867–1889.

Statistical properties of endomorphisms and  compact group extensions, I. Melbourne and M. Nicol. J. London Math. Soc. (2) 70 (2004), no. 2, 427–446.

Random iteration of Euclidean isometries,  M. Adahl, I. Melbourne and M. Nicol. (2003)

Statistical properties of compact group  extensions of hyperbolic flows and their time-one maps, M. Field, I. Melbourne, M. Nicol and A. Torok. Discrete Contin. Dyn. Syst. 12 (2005), no. 1, 79–96.

Statistical limit laws for equivariant observations, I. Melbourne and M. Nicol. Stoch. Dyn. 4 (2004), no. 1, 1–13.

Livsic regularity for Markov systems H. Bruin, M. Holland and   M. Nicol. Ergodic Theory Dynam. Systems 25 (2005), no. 6, 1739–1765.

Almost sure invariance principle for  nonuniformly hyperbolic systems, I. Melbourne and   M. Nicol. Comm. Math. Phys. 260 (2005), no. 1, 131–146.

Whitney regularity for solutions to the  coboundary equation on Cantor sets, M. Nicol and A. Torok.Math. Phys. Electron. J. 13 (2007), Paper 6, 20 pp.

A vector-valued almost sure  invariance principle for hyperbolic dynamical systems,  I. Melbourne and   M. Nicol. Ann. Probab. 37 (2009), no. 2, 478–505.

Large deviations for nonuniformly hyperbolic systems, I. Melbourne and   M. Nicol. Trans. Amer. Math. Soc. 360 (2008), no. 12, 6661–6676.

Extreme value distributions for non-uniformly expanding systems,  M. Holland, M. Nicol and A. Torok. Trans. Amer. Math. Soc. 364 (2012), no. 2, 661–688.

On Young Towers associated with infinite measure preserving transformations, H. Bruin, M. Nicol and D. Terhesiu. Stoch. Dyn. 9 (2009), no. 4, 635–655.

Extreme value theory  and return time statistics for  dispersing billiard maps and flows, Lozi maps and Lorenz-like map, C. Gupta, M. Holland and M. Nicol. Ergodic Theory Dynam. Systems 31 (2011), no. 5, 1363–1390.

A Borel-Cantelli lemma for non-uniformly expanding dynamical systems, C. Gupta, M. Nicol  and   W. Ott. Nonlinearity 23 (2010), no. 8, 1991–2008.

Smooth Livsic regularity for piecewise expanding maps, M. Nicol and T. Persson. Proc. Amer. Math. Soc. 140 (2012), no. 3, 905–914.

A note on Borel-Cantelli lemmas for non-uniformly hyperbolic dynamical systems, N. Haydn, M. Nicol, T. Persson and S. Vaienti. Ergodic Theory Dynam. Systems 33 (2013), no. 2, 475–498.

Erdos Renyi laws for dynamical systems M. Denker and  M. Nicol. J. Lond. Math. Soc. (2) 87 (2013), no. 2, 497–508.

Central limit theorems for the shrinking target problem, N. Haydn, M. Nicol, S. Vaienti and L.Zhang. J. Stat. Phys. 153 (2013), no. 5, 864–887.

Convergence of rare events point processes to  the Poisson for billiards,  N. Haydn, J. Freitas and M. Nicol. Nonlinearity 27 (2014), no. 7, 1669–1687.

Speed of convergence to an extreme value distribution for a non-uniformly hyperbolic dynamical system,  M.Holland and M. Nicol. Stoch. Dyn. 15 (2015), no. 4, 1550028, 23 pp.

Annealed and quenced limit theorems for random expanding dynamical systems, R. Aimino,  M. Nicol and S. Vaienti. Probab. Theory Related Fields 162 (2015), no. 1-2, 233–274.

Polynomial loss of memory for maps of the interval with a neutral fixed point, R. Aimino,  H.Hu, M. Nicol, A. Torok  and S. Vaienti. Discrete Contin. Dyn. Syst. 35 (2015), no. 3, 793–806.

Extremal dichotomy for hyperbolic toral automorphisms, M. Carvalho, A. C. M. Freitas, J. M. Freitas, M. Holland and M. Nicol. Dyn. Syst. 30 (2015), no. 4, 383–403.

Almost sure invariance principle for sequential and non-stationary dynamical systems, N. Haydn, M. Nicol, A. Torok and S. Vaienti. Trans. Amer. Math. Soc. 369 (2017), no. 8, 5293–5316.

Recurrence statistics for the space of Interval Exchange maps and the Teichmüller flow on the space of translation surfaces, R. Aimino, M. Nicol and M. Todd. Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017), no. 3, 1371–1401.

Almost sure convergence of maxima for chaotic dynamical systems, M. Holland, M. Nicol and A. Torok. Stochastic Process. Appl. 126 (2016), no. 10, 3145–3170.

Central limit theorems for sequential and random intermittent dynamical systems, M. Nicol, A. Torok and S. Vaienti. Ergodic Theory Dynam. Systems 38 (2018), no. 3, 1127–1153.

Dynamical Borel-Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems, M. Carney and M. Nicol. Nonlinearity 30 (2017), no. 7, 2854–2870.

Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems, M. Carney, M. Nicol and H. K. Zhang. J. Stat. Phys. 169 (2017), no. 4, 804–823.

Large-deviation probabilities for correlated Gaussian processes and intermittent dynamical systems, M. Massah, M. Nicol and H. Kantz. (2018)

A note on large deviations for unbounded observables,  M. Nicol and A. Torok. Stoch. Dyn. 20 (2020), no. 5, 2050030, 21 pp.

Martingale approximations and  anisotropic Banach spaces with an application to the time-one map of a Lorentz gas, M. Demers, I. Melbourne and M. Nicol. (2020) Nonlinearity 33 (2020), no. 8, 4095–4113.

Large deviations and central limit theorems for sequential and random systems of intermittent maps, M. Nicol, F. Pereira and M. Torok. Ergodic Theory Dynam. Systems 41 (2021), no. 9, 2805–2832.

Extremes and extremal indices for level set observables on hyperbolic systems, M. Carney, M. Holland and M. Nicol. Nonlinearity 34 (2021), no. 2, 1136–1167.

Erdos-Renyi laws for polynomially and exponentially mixing dynamical systems. N. Haydn and M. Nicol. Proc AMS, Volume 151, Number 8, August 2023, 3415-3430.

Birkhoff sum convergence of Frechet observables to stable laws in Gibbs-Markov systems and applications. A. Chen, M. Nicol and A. Torok. Nonlinearity 38 (2025), no. 5, Paper No. 055030, 27 pp.

Stable laws for random dynamical systems. R. Aimino, M. Nicol and A. Torok. Ergodic Theory Dynam. Systems 44 (2024), no. 11, 3041-3090.

Symmetry of attractors and the Karhunen-Loeve decomposition M. Dellnitz, M. Golubitsky and M. Nicol. Appl. Math. Sci., 100

Springer-Verlag, New York, 1994, 73–108.

A note on symmetries of invariant sets with compact group actions M. Field, M. Golubitsky and M. Nicol. Tatra Mt. Math. Publ. 4 (1994), 93–104.

Symmetry detectives for SBR attractors  M. Golubitsky and M. Nicol. Nonlinearity 8 (1995), no. 6, 1027–1037.

On symmetric omega-limit sets in reversible flows  J. S. W. Lamb and M. Nicol. Progr. Nonlinear Differential Equations Appl., 19

Birkhäuser Verlag, Basel, 1996, 103–120.

Symmetries of periodic solutions for planar potential systems M. Golubitsky, J.-M. Mao and M. Nicol. Proc. Amer. Math. Soc. 124 (1996), no. 10, 3219–3228.

Symmetric attractors for diffeomorphisms and flows  M. J. Field, I. Melbourne and M. Nicol. Proc. London Math. Soc. (3) 72 (1996), no. 3, 657–696.

Symmetries of the asymptotic dynamics of random compositions of equivariant maps M. Nicol. Nonlinearity 9 (1996), no. 1, 225–235.

Detection of symmetry of attractors from observations- theory  P. Ashwin and M. Nicol. Phys. D 100 (1997), no. 1-2, 58–70.

On symmetric attractors in reversible dynamical systems J. S. W. Lamb and M. Nicol. Phys. D 112 (1998), no. 1-2, 281–297.

Drift bifurcations of relative equilibria and  transitions of spiral waves P. Ashwin, I. Melbourne and M. Nicol. Nonlinearity 12 (1999), no. 4, 741–755.

Hypermeander of Spirals; Local Bifurcations and Statistical Properties P. Ashwin, I. Melbourne and M. Nicol. Phys. D 156 (2001), no. 3-4, 364–382.

Drift for Euclidean extensions of dynamical systems  P. Ashwin, I. Melbourne and M. Nicol. World Scientific Publishing Co., Inc., River Edge, NJ, 2000, 145–150.

Random and deterministic perturbation of a class of skew products D. Hadjiloucas, D. S. Broomhead and M. Nicol. Dynam. Stability Systems 14 (1999), no. 2, 115–128.

On the unfolding of a blowout bifurcation P. Ashwin, P. Aston and M. Nicol. Phys. D 111 (1998), no. 1-4, 81–95.

Acceleration of one-dimensional mixing by permutation. P. Ashwin, M. Nicol and N. Kirby. Phys. A 310 (2002), no. 3-4, 347–363.

On the nature of Benford's Law G. Gottwald and M. Nicol. Phys. A 303 (2002), no. 3-4, 387–396.

Periodicity and Recurrence in Piecewise Rotations of Euclidean Spaces M. Mendes and M. Nicol. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 14 (2004), no. 7, 2353–2361.

Some Curious Phenomena in Coupled Cell Networks M.Golubitsky,  M. Nicol and I. Stewart. J. Nonlinear Sci. 14 (2004), no. 2, 207–236.

Variable Step Random Walks and Self-Similar Distributions G. Gunaratne,  J. McCauley,  Matthew Nicol and A. Torok. J. Stat. Phys. 121 (2005), no. 5-6, 887–899.

Generation of multi-scroll attractors without equilibria via piecewise linear systems  (2017) R. J Escalante, E. Campos-Canton and M. Nicol. Chaos 27 (2017), no. 5, 053109, 8 pp.

Itinerary synchronization between PWL systems coupled with unidirectional links. A. Anzo-Hernandez, E. Campos-Canton and M. Nicol. Commun. Nonlinear Sci. Numer. Simul. 70 (2019), 102–124.

Non-stationarity of  summer temperature extremes in Texas. R. Azencott, M. Carney  and M. Nicol. International  Journal of  Climatology. 2020;40:620–640.

Analysis and simulation of extremes and rare events in complex systems. M. Carney, H. Kantz  and M. Nicol. Stud. Syst. Decis. Control, 304, Springer, Cham, 2020, 151–182.

An analytical, numerical and experimental study of in-vitro SARS-COV-2 evolution in Vero B4 cells. M. Nicol, J. Sng, Y. Zhu, S. Sonnleitner, K Short and M. Carney. Journal of Theoretical Biology, 2025 Feb 7:598:112000

Hurrricane simulation and non-stationary extremal analysis for a changing climate. M. Carney, H. Kantz and M. Nicol. Journal of Applied Meterology and Climatology. Volume 61, Issue 11, 2020, 1635-1648

Algorithm for planning a double-jaw orthognathic surgery using computer-aided surgical simulation (CASS) protocol: 2. Three-dimensional cephalometry   J. Xia, J. Gateno, J. F. Teichgraeber, P. Yuan, J. Li, K.-C. Chen, A. Jajoo, M. Nicol, D. M. Alfi. Int J Oral Maxillofac Surg. 2015 December ; 44(12): 1441–1450. 

The primal sagittal plane of the head: a new concept.  J. Gateno, A. Jajoo, M. Nicol, J.J. Xia. Int J Oral Maxillofac Surg. 2016 March ; 45(3): 399–405.