Dr Ian Morris
Reader in Mathematics
Director of the Mathematics MSc
School of Mathematical Sciences
Queen Mary University of London
Queen Mary University of London
Research
Ergodic theory, Fractal geometry, Matrix analysis
Publications
Publications of specific relevance to the Centre for Complex Systems2024
Morris ID (2024). A Stability Dichotomy for Discrete-Time Linear Switching Systems in Dimension Two. SIAM Journal on Control and Optimization, Society for Industrial & Applied Mathematics (SIAM) vol. 62 (1), 400-414. 31-01-2024
Morris I (2024). An irreducible linear switching system whose unique Barabanov norm is not strictly convex. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics 10-01-2024
2023
Morris ID and Varney J (2023). A note on the marginal instability rates of two-dimensional linear cocycles. Dynamical Systems, Taylor & Francis 21-06-2023
2022
Morris ID and Sert Ç (2022). A converse statement to Hutchinson’s theorem and a dimension gap for self-affine measures. Journal of the European Mathematical Society, European Mathematical Society - EMS - Publishing House vol. 25 (11), 4315-4367. 11-11-2022
Morris ID (2022). On affine iterated function systems which robustly admit an invariant affine subspace. Proceedings of the American Mathematical Society, American Mathematical Society (AMS) vol. 151 (01), 101-112. 07-10-2022
Morris ID (2022). On dense intermingling of exact overlaps and the open set condition. Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP) vol. 65 (3), 747-759. 01-08-2022
Morris ID (2022). Fast approximation of the affinity dimension for dominated affine iterated function systems. Annales Fennici Mathematici, Finnish Mathematical Society vol. 47 (2), 645-694. 13-04-2022
Morris I (2022). Marginally unstable discrete-time linear switched systems with highly irregular trajectory growth. Systems and Control Letters, Elsevier 11-04-2022
Morris I (2022). Fast approximation of the p-radius, matrix pressure or generalised Lyapunov exponent for positive and dominated matrices. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics 10-02-2022
2021
Morris ID and Sert C (2021). A strongly irreducible affine iterated function system with two invariant measures of maximal dimension. Ergodic Theory and Dynamical Systems vol. 41 (11), 3417-3438. 30-11-2021
Morris I and Jurga N (2021). How long is the Chaos Game? Bulletin of the London Mathematical Society, London Mathematical Society 20-09-2021
Morris ID (2021). Totally Ergodic Generalised Matrix Equilibrium States have the Bernoulli Property. Communications in Mathematical Physics, Springer Nature vol. 387 (2), 995-1050. 14-09-2021
Fraser JM, Lee LD, Morris ID and Yu H (2021). Lq-spectra of self-affine measures: Closed forms, counterexamples, and split binomial sums. Nonlinearity vol. 34 (9), 6331-6357. 01-09-2021
Morris ID (2021). Prevalent uniqueness in ergodic optimisation. Proceedings of the American Mathematical Society, American Mathematical Society 09-02-2021
2020
Bárány B, Käenmäki A and Morris ID (2020). Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles. Israel Journal of Mathematics, Springer Nature vol. 239 (1), 173-214. 01-08-2020
Jurga N and Morris ID (2020). Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone. Nonlinearity, IOP Publishing vol. 33 (4), 1572-1593. 17-02-2020
2019
Jurga N and Morris I (2019). Effective estimates on the top Lyapunov exponents for random matrix products. Nonlinearity, IOP Publishing vol. 32 (11), 4117-4146. 26-09-2019
Blumenthal A and Morris ID (2019). Characterization of dominated splittings for operator cocycles acting on Banach spaces. Journal of Differential Equations, Elsevier vol. 267 (7), 3977-4013. 01-09-2019
Morris ID (2019). An explicit formula for the pressure of box-like affine iterated function systems. Journal of Fractal Geometry, European Mathematical Society - EMS - Publishing House vol. 6 (2), 127-141. 21-03-2019
2018
Morris ID and Shmerkin P (2018). On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems. Transactions of the American Mathematical Society, American Mathematical Society (AMS) vol. 371 (3), 1547-1582. 17-10-2018
Morris ID (2018). Some observations on Käenmäki measures. Annales Academiae Scientiarum Fennicae Mathematica, Finnish Mathematical Society vol. 43, 945-960. 01-08-2018
Bochi J and Morris ID (2018). Equilibrium states of generalised singular value potentials and applications to affine iterated function systems. Geometric and Functional Analysis, Springer Nature vol. 28 (4), 995-1028. 24-04-2018
2017
MORRIS ID (2017). A necessary and sufficient condition for a matrix equilibrium state to be mixing. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP) vol. 39 (8), 2223-2234. 04-12-2017
Käenmäki A and Morris ID (2017). Structure of equilibrium states on self‐affine sets and strict monotonicity of affinity dimension. Proceedings of the London Mathematical Society, Wiley vol. 116 (4), 929-956. 30-11-2017
Morris ID (2017). Generic properties of the lower spectral radius for some low-rank pairs of matrices. Linear Algebra and its Applications, Elsevier vol. 524, 35-60. 01-07-2017
MORRIS ID (2017). Lyapunov-maximizing measures for pairs of weighted shift operators. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP) vol. 39 (1), 225-247. 04-05-2017
MORRIS ID (2017). Ergodic properties of matrix equilibrium states. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP) vol. 38 (6), 2295-2320. 14-03-2017
Morris ID (2017). On Falconer's formula for the generalised Rényi dimension of a self-affine measure. Annales Academiae Scientiarum Fennicae Mathematica, Finnish Mathematical Society vol. 42, 227-238. 01-02-2017
2016
Morris ID (2016). An inequality for the matrix pressure function and applications. Advances in Mathematics, Elsevier vol. 302, 280-308. 01-10-2016
Morris ID (2016). A rigorous version of R.P. Brent's model for the binary Euclidean algorithm. Advances in Mathematics, Elsevier vol. 290, 73-143. 01-02-2016
2015
Morris ID (2015). A note on configurations in sets of positive density which occur at all large scales. Israel Journal of Mathematics, Springer Nature vol. 207 (2), 719-738. 28-03-2015
2014
Bochi J and Morris ID (2014). Continuity properties of the lower spectral radius. Proceedings of the London Mathematical Society, Wiley vol. 110 (2), 477-509. 02-12-2014
2013
Morris ID and Sidorov N (2013). On a devil’s staircase associated to the joint spectral radii of a family of pairs of matrices. Journal of the European Mathematical Society, European Mathematical Society - EMS - Publishing House vol. 15 (5), 1747-1782. 21-07-2013
HARE KG, MORRIS ID and SIDOROV N (2013). Extremal sequences of polynomial complexity. Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press (CUP) vol. 155 (2), 191-205. 02-05-2013
Morris ID (2013). Mather sets for sequences of matrices and applications to the study of joint spectral radii. Proceedings of the London Mathematical Society, Wiley vol. 107 (1), 121-150. 16-01-2013
2012
Morris ID (2012). The generalised Berger–Wang formula and the spectral radius of linear cocycles. Journal of Functional Analysis, Elsevier vol. 262 (3), 811-824. 01-02-2012
Morris ID (2012). A New Sufficient Condition for the Uniqueness of Barabanov Norms. SIAM Journal on Matrix Analysis and Applications, Society for Industrial & Applied Mathematics (SIAM) vol. 33 (2), 317-324. 01-01-2012
2011
Hare KG, Morris ID, Sidorov N and Theys J (2011). An explicit counterexample to the Lagarias–Wang finiteness conjecture. Advances in Mathematics, Elsevier vol. 226 (6), 4667-4701. 01-04-2011
2010
Morris ID (2010). A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory. Advances in Mathematics, Elsevier vol. 225 (6), 3425-3445. 01-12-2010
Morris ID (2010). Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms. Linear Algebra and its Applications, Elsevier vol. 433 (7), 1301-1311. 01-12-2010
Morris ID (2010). Ergodic optimization for generic continuous functions. Discrete and Continuous Dynamical Systems, American Institute of Mathematical Sciences (AIMS) vol. 27 (1), 383-388. 01-01-2010
2009
MORRIS ID (2009). The Mañé–Conze–Guivarc’h lemma for intermittent maps of the circle. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP) vol. 29 (5), 1603-1611. 03-02-2009
2008
Jenkinson O and Morris ID (2008). Lyapunov optimizing measures for C-1 expanding maps of the circle. ERGOD THEOR DYN SYST, Cambridge Journals vol. 28 (6), 1849-1860. 01-12-2008
COLLIER D and MORRIS ID (2008). Approximating the maximum ergodic average via periodic orbits. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP) vol. 28 (4), 1081-1090. 01-08-2008
Morris ID (2008). Maximizing measures of generic Hölder functions have zero entropy. Nonlinearity, IOP Publishing vol. 21 (5), 993-1000. 04-04-2008
2007
Morris ID (2007). A sufficient condition for the subordination principle in ergodic optimization. Bulletin of the London Mathematical Society, Wiley vol. 39 (2), 214-220. 13-02-2007
Morris ID (2007). Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type. Journal of Statistical Physics, Springer Nature vol. 126 (2), 315-324. 01-01-2007