Dr Ian Morris
Reader in Mathematics
Director of the Mathematics MSc
School of Mathematical Sciences
Queen Mary University of London
Research
Ergodic theory, Fractal geometry, Matrix analysis
Publications
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Publications of specific relevance to the Centre for Complex Systems
2024
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 10-01-20242023
Morris ID and Varney J (2023).
A note on the marginal instability rates of two-dimensional linear cocycles. Dynamical Systems,
Taylor & Francis 21-06-20232022
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 10-02-20222021
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![bullet icon](/common/publications/images/bullet24.png)
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 09-02-20212020
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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![bullet icon](/common/publications/images/bullet24.png)
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
Morris ID and Sert CAGRI (2020).
A strongly irreducible affine iterated function system with two invariant measures of maximal dimension. Ergodic Theory and Dynamical Systems 01-01-20202019
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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![bullet icon](/common/publications/images/bullet24.png)
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 I (2019).
An explicit formula for the pressure of box-like affine iterated function systems. Journal of Fractal Geometry,
European Mathematical Society - EMS - Publishing House GmbH vol. 6 (2), 127-141.
01-01-20192018
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![Relevant Publication](/common/publications/images/fav.png)
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.
24-04-20182017
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![Relevant Publication](/common/publications/images/fav.png)
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.
01-02-20172016
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.
01-02-20162015
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.
28-03-20152014
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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.
02-12-20142013
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 GmbH vol. 15 (5), 1747-1782.
21-07-2013![bullet icon](/common/publications/images/bullet24.png)
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.
16-01-20132012
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.
01-01-20122011
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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.
01-04-20112010
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![bullet icon](/common/publications/images/bullet24.png)
D. Morris I (2010).
Ergodic optimization for generic continuous functions. Discrete and Continuous Dynamical Systems,
American Institute of Mathematical Sciences (AIMS) vol. 27 (1), 383-388.
01-01-20102009
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.
03-02-20092008
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![bullet icon](/common/publications/images/bullet24.png)
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.
04-04-20082007
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