Selected Publications

Ergodic theory of equivariant diffeomorphisms M. Field and M. Nicol, Memoirs of American Mathematical Society, Vol 169, Number 803, (2004).

Ergodic Theory: Basic Examples and Constructions M. Nicol and K. Petersen, a chapter in the Encyclopedia of Complexity and System Science [709] (2009).

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, Wiley (2016) 312 pages.

Stochastic stability of Bernoulli toral linked twist maps of finite and infinite entropy,   M. Nicol, Ergod. Th. Dynam. Sys. 16 (1996) 493-518.

A Bernoulli toral linked twist map without positive Lyapunov exponents,   M. Nicol, Proc. Amer. Math. Soc. 124, 4, (1996), 1253-1263.

Induced maps of Bernoulli dynamical systems,   M. Nicol, Discrete and Continuous Dynamical Systems 7 No. 1 (2001), 147-154.

Measurable cocycle rigidity for some noncompact groups,   M. Nicol and M. Pollicott, Bull. London. Math. Soc. 31 (1999), 592-600.

Livsic's Theorem for Semisimple Lie groups,   M. Nicol and M. Pollicott, Erg. Th. Dyn. Sys. 21 (2001) 1501-1509.

Euclidean extensions of Dynamical Systems,   M. Nicol, I. Melbourne and P. Ashwin, Nonlinearity ,Vol 14, 275-300, (2001)

Regularity of invariant graphs over hyperbolic systems,   D. Hadjiloucas, M. Nicol and C. Walkden, Erg. Th. Dyn. Sys. 22 (2002), 469-482

On the fine structure of stationary measures in systems which contract-on-average,   M. Nicol, N. Sidorov and D. Broomhead, Journal of Theoretical Probability 15-3 (2002), 715-730.

Stable transitivity of Euclidean group extensions,   I. Melbourne and M. Nicol, Erg. Thy. Dyn. Sys. 23 (2003), no. 2, 611-619.

Livsic Theorems for group extensions of hyperbolic systems with singularities   M. Nicol and A. Scott, Erg. Thy. Dyn. Sys. 23 (2003), no. 6, 1867-1889.

Statistical properties of endomorphisms and compact group extensions I. Melbourne and M. Nicol, Proceedings of the LMS (2) 70 (2004) 427-446

Random iteration of Euclidean isometries   M. Adahl, I. Melbourne and M. Nicol, Nonlinearity 16 (2003) no.3, 977-987.

Statistical properties of compact group extensions of hyperbolic flows and their time-one maps   M. Field, I. Melbourne, M. Nicol and A. Torok, Discrete and Continuous Dynamical Systems 12-1 (2005), 79-96.

Statistical limit laws for equivariant observations   I. Melbourne and M. Nicol, Stochastics and Dynamics 4 (2004), 1-13.

Livsic regularity for Markov systems   H. Bruin, M. Holland and M. Nicol, Ergodic Theory and Dynamical Systems 25 (2005), 1739-1765.

Almost sure invariance principle for nonuniformly hyperbolic systems   I. Melbourne and M. Nicol, Communications in Mathematical Physics 260 (2005), 131-146.

Whitney regularity for solutions to the coboundary equation on Cantor sets   M. Nicol and A. Torok Mathematical Physics Electronic Journal 13 2007

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

Large deviations for nonuniformly hyperbolic systems   I. Melbourne and M. Nicol, Trans AMS 360 (2008), 6661-6676

Extreme value distributions for non-uniformly expanding systems   M. Holland, M. Nicol and A. Torok Transactions AMS 364 (2012), 661-688.

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

Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. C. Gupta, M. Holland and M. Nicol Ergodic Theory and Dynamical Systems 31-5 (2011) 1361--1390

A Borel-Cantelli lemma for non-uniformly expanding dynamical systems C. Gupta, M. Nicol and W. Ott Nonlinearity 23-8 (2010) 1991-2008.

Smooth Livsic regularity for piecewise expanding maps M. Nicol and T. Persson, Proc AMS 140 no.3 (2012) 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 and Dynamical Systems 33 no.2 (2013) 475-498.

Erdös-Rényi limit laws for hyperbolic dynamical systems M. Denker and M. Nicol Journal LMS 87 (2) (2013) 497-508

Central limit theorems for the shrinking target problem N. Haydn, M. Nicol, S. Vaienti and L.Zhang Journal of Statistical Physics (2013) 153: 864-887

Convergence of rare events point processes to the Poisson for billiards N. Haydn, J. Freitas and M. Nicol Nonlinearity, 27, (2014) 1669-1687

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

Annealed and quenced limit theorems for random expanding dynamical systems R. Aimino, M. Nicol and S. Vaienti Probability Theory and Related Fields, 162 (1), 233-274, (2015)

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 and Continuous Dynamical Systems, A, 35, 3, 793-806, (2015)

Extremal dichotomy for hyperbolic toral automorphisms M. Carvalho, A. C. M. Freitas, J. M. Freitas, M. Holland and M. Nicol. Dynamical Systems: An International Journal Volume 30, No. 4, 383-403, (2015).

Almost sure invariance principles for sequential and non-stationary dynamical systems N. Haydn, M. Nicol, A. Torok and S. Vaienti Transactions of the AMS, 369 , 5293-5316, (2017)

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 Annales de l'Institut Henri Poincarè Serie (B) Probabilitès et Statistiques, 53 (3), 1371-1401, (2017)

Almost sure convergence of maxima for chaotic dynamical systems'' M. Holland, M. Nicol and A. Torok Stochastic Processes and their Applications, 126, no. 10, 3145-3170, (2016)

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

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, no. 7, 2854-2870, (2017)

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

Large-deviation probabilities for correlated Gaussian processes and intermittent dynamical systems. M. Massah, M. Nicol and H. Kantz Physical Review E, 97, no. 5, 052147, (2018)

A note on large deviations for unbounded observables. M. Nicol and A. Torok Stochastics and Dynamics, 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 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 to appear Ergodic Theory and Dynamical Systems

Extremes and extremal indices for level set observables on hyperbolic systems. M. Carney, M. Holland and M. Nicol to appear Nonlinearity

Symmetry detectives for SBR attractors,   M. Golubitsky and M. Nicol, Nonlinearity 8 (1995) 1027-1037.

Symmetry of attractors and the Karhunen-Loeve decomposition,   M. Dellnitz, M. Golubitsky and M. Nicol, In: Trends and Perspectives in Applied Mathematics (L. Sirovich, ed.) 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, In: Equadiff 8. Tatra Mountains Math. Publ. 4 (1994) 93-104.

Symmetries of periodic solutions for planar potential systems,   M. Golubitsky, J.-M. Mao and M. Nicol, . Proc. Amer. Math. Soc. 124 (1996) 3219-3228.

Symmetric attractors for diffeomorphisms and flows,   M. J. Field, I. Melbourne and M. Nicol, Proc. London Math. Soc., 72 (1996) 657-696.

Symmetries of the asymptotic dynamics of random compositions of equivariant maps,   M. Nicol, Nonlinearity, 9 (1996) 225-235.

Detection of symmetry of attractors from observations- theory,   P. Ashwin and M. Nicol, Physica D, 100 (1997) 58-70.

On symmetric omega-limit sets in reversible flows,   J. S. W. Lamb and M. Nicol, Nonlinear Dynamical Systems and Chaos, H. W. Broer, S. A. van Gils, I. Hoveijn, F. Takens (eds), Progress in Nonlinear Partial Differential Equations and Applications, Birkhauser, (1995).

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

Drift bifurcations of relative equilibria and transitions of spiral waves,   P. Ashwin, I. Melbourne and M. Nicol, Nonlinearity, Vol 12, 741-755, (1999)

Hypermeander of Spirals; Local Bifurcations and Statistical Properties,   P. Ashwin, I. Melbourne and M. Nicol, Physica D , 156 (2001) 364-382.

Drift for Euclidean extensions of dynamical systems   P. Ashwin, I. Melbourne and M. Nicol, Equadiff 99, International conference on dynamical systems (B. Fiedler et al eds) , World Scientific, Singapore, 2000, 145-150.

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

On the unfolding of a blowout bifurcation,   P. Ashwin, P. Aston and M. Nicol, Physica D. 111 (1998), 81-95.

Acceleration of one-dimensional mixing by permutation,   P. Ashwin, M. Nicol and N. Kirby, Physica A 310 (2002), 347-362

On the nature of Benford's Law,   G. Gottwald and M. Nicol, Physica A 303 (2002), 387-396.

Piecewise isometries of Euclidean Spaces,   M. Mendes and M. Nicol, I. J. Bifurcation and Chaos 14(7): 2353-2361 (2004)

Some Curious Phenomena in Coupled Cell Networks   M. Golubitsky, M. Nicol and I. Stewart, Journal of Nonlinear Science 14 (2004), 207-236.

Variable Step Random Walks and Self-Similar Distributions   G. Gunaratne, J. McCauley, Matthew Nicol and A. Torok, Journal of Statistical Physics 121 No. 5-6 (2005), 887-899.

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

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

Non-stationarity of summer temperature extremes in Texas. R. Azencott, M. Carney and M. Nicol International Journal of Climatology. Vol. 40, Issue 1, 620-640, (2020).

Analysis and simulation of extremes and rare events in complex systems. M. Carney, H. Kantz and M. Nicol Advances in dynamics, optimization and computation. Studies in systems, decision and control. Springer (2020).

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, International Journal of Oral and Maxillofacial Surgery Vol. 44, Issue 12, p1441-1450 December 2015.

The primal sagittal plane of the head: a new concept. J. Gateno, A. Jajoo, M. Nicol, J.J. Xia. International Journal of Oral and Maxillofacial Surgery Accepted and published online: December 18 2015.