Ergodic theory and Probability

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.

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

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 to appear Mathematical Physics Electronic Journal

A vector-valued almost sure invariance principle for hyperbolic dynamical systems   I. Melbourne and M. Nicol, to appear Annals of Probability

Large deviations for nonuniformly hyperbolic systems   I. Melbourne and M. Nicol, to appear Trans AMS

Extreme value distributions for non-uniformly hyperbolic dynamical systems   M. Holland, M. Nicol and A. Torok preprint


Equivariant dynamical systems

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.


Chaotic dynamics, coupled cell systems, iterated function systems and other topics.

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, to appear International Journal of Bifurcation and Chaos (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.

A theory of fluctuations in stock prices   A. Alejandro-Quinones, K. Bassler, M. Field, J. McCauley, M. Nicol. I. Timofyev, A. Torok and G. Gunaratne. Physica A 362 No. 2 (2006), 383-392