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Research

Publications: Dr Ian Morris

Morris ID ( 2022 ) . On affine iterated function systems which robustly admit an invariant affine subspace . Proceedings of the American Mathematical Society vol. 151 , ( 01 ) 101 - 112 .
Morris I ( 2022 ) . Marginally unstable discrete-time linear switched systems with highly irregular trajectory growth . Systems and Control Letters
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
Morris ID ( 2022 ) . Fast approximation of the affinity dimension for dominated affine iterated function systems . Annales Fennici Mathematici vol. 47 , ( 2 ) 645 - 694 .
Morris ID, 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 .
Morris ID ( 2021 ) . Totally Ergodic Generalised Matrix Equilibrium States have the Bernoulli Property . Communications in Mathematical Physics vol. 387 , ( 2 ) 995 - 1050 .
Morris I, Jurga N ( 2021 ) . "How long is the Chaos Game?" . Bulletin of the London Mathematical Society
Fraser JM, Lee LD, Morris ID, Yu H ( 2021 ) . L<sup>q</sup>-spectra of self-affine measures: Closed forms, counterexamples, and split binomial sums . Nonlinearity vol. 34 , ( 9 ) 6331 - 6357 .
Morris ID ( 2021 ) . Prevalent uniqueness in ergodic optimisation . Proceedings of the American Mathematical Society
Bárány B, Käenmäki A, Morris ID ( 2020 ) . Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles . Israel Journal of Mathematics vol. 239 , ( 1 ) 173 - 214 .
Jurga N, Morris ID ( 2020 ) . Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone . Nonlinearity vol. 33 , ( 4 ) 1572 - 1593 .
Morris ID, Sert CAGRI ( 2020 ) . A strongly irreducible affine iterated function system with two invariant measures of maximal dimension . Ergodic Theory and Dynamical Systems
Jurga N, Morris I ( 2019 ) . Effective estimates on the top Lyapunov exponents for random matrix products . Nonlinearity vol. 32 , ( 11 ) 4117 - 4146 .
Blumenthal A, Morris ID ( 2019 ) . Characterization of dominated splittings for operator cocycles acting on Banach spaces . Journal of Differential Equations vol. 267 , ( 7 ) 3977 - 4013 .
Morris I ( 2019 ) . An explicit formula for the pressure of box-like affine iterated function systems . Journal of Fractal Geometry vol. 6 , ( 2 ) 127 - 141 .
Morris ID, Shmerkin P ( 2018 ) . On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems . Transactions of the American Mathematical Society vol. 371 , ( 3 ) 1547 - 1582 .
Morris ID ( 2018 ) . Some observations on Käenmäki measures . Annales Academiae Scientiarum Fennicae Mathematica vol. 43 , 945 - 960 .
Bochi J, Morris ID ( 2018 ) . Equilibrium states of generalised singular value potentials and applications to affine iterated function systems . Geometric and Functional Analysis vol. 28 , ( 4 ) 995 - 1028 .
MORRIS ID ( 2017 ) . A necessary and sufficient condition for a matrix equilibrium state to be mixing . Ergodic Theory and Dynamical Systems vol. 39 , ( 8 ) 2223 - 2234 .
Käenmäki A, Morris ID ( 2017 ) . Structure of equilibrium states on self‐affine sets and strict monotonicity of affinity dimension . Proceedings of the London Mathematical Society vol. 116 , ( 4 ) 929 - 956 .
Morris ID ( 2017 ) . Generic properties of the lower spectral radius for some low-rank pairs of matrices . Linear Algebra and its Applications vol. 524 , 35 - 60 .
MORRIS ID ( 2017 ) . Lyapunov-maximizing measures for pairs of weighted shift operators . Ergodic Theory and Dynamical Systems vol. 39 , ( 1 ) 225 - 247 .
MORRIS ID ( 2017 ) . Ergodic properties of matrix equilibrium states . Ergodic Theory and Dynamical Systems vol. 38 , ( 6 ) 2295 - 2320 .
Morris ID ( 2017 ) . On Falconer's formula for the generalised Rényi dimension of a self-affine measure . Annales Academiae Scientiarum Fennicae Mathematica vol. 42 , 227 - 238 .
Morris ID ( 2016 ) . An inequality for the matrix pressure function and applications . Advances in Mathematics vol. 302 , 280 - 308 .
Morris ID ( 2016 ) . A rigorous version of R.P. Brent's model for the binary Euclidean algorithm . Advances in Mathematics vol. 290 , 73 - 143 .
Morris ID ( 2015 ) . A note on configurations in sets of positive density which occur at all large scales . Israel Journal of Mathematics vol. 207 , ( 2 ) 719 - 738 .
Bochi J, Morris ID ( 2014 ) . Continuity properties of the lower spectral radius . Proceedings of the London Mathematical Society vol. 110 , ( 2 ) 477 - 509 .
HARE KG, MORRIS ID, SIDOROV N ( 2013 ) . Extremal sequences of polynomial complexity . Mathematical Proceedings of the Cambridge Philosophical Society vol. 155 , ( 2 ) 191 - 205 .
Morris ID ( 2013 ) . Mather sets for sequences of matrices and applications to the study of joint spectral radii . Proceedings of the London Mathematical Society vol. 107 , ( 1 ) 121 - 150 .
Morris I, 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 vol. 15 , ( 5 ) 1747 - 1782 .
Morris ID ( 2012 ) . The generalised Berger–Wang formula and the spectral radius of linear cocycles . Journal of Functional Analysis vol. 262 , ( 3 ) 811 - 824 .
Morris ID ( 2012 ) . A New Sufficient Condition for the Uniqueness of Barabanov Norms . SIAM Journal on Matrix Analysis and Applications vol. 33 , ( 2 ) 317 - 324 .
Hare KG, Morris ID, Sidorov N, Theys J ( 2011 ) . An explicit counterexample to the Lagarias–Wang finiteness conjecture . Advances in Mathematics vol. 226 , ( 6 ) 4667 - 4701 .
Morris ID ( 2010 ) . A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory . Advances in Mathematics vol. 225 , ( 6 ) 3425 - 3445 .
Morris ID ( 2010 ) . Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms . Linear Algebra and its Applications vol. 433 , ( 7 ) 1301 - 1311 .
D. Morris I ( 2010 ) . Ergodic optimization for generic continuous functions . Discrete and Continuous Dynamical Systems vol. 27 , ( 1 ) 383 - 388 .
MORRIS ID ( 2009 ) . The Mañé–Conze–Guivarc’h lemma for intermittent maps of the circle . Ergodic Theory and Dynamical Systems vol. 29 , ( 5 ) 1603 - 1611 .
Jenkinson O, Morris ID ( 2008 ) . Lyapunov optimizing measures for C-1 expanding maps of the circle . ERGOD THEOR DYN SYST vol. 28 , ( 6 ) 1849 - 1860 .
COLLIER D, MORRIS ID ( 2008 ) . Approximating the maximum ergodic average via periodic orbits . Ergodic Theory and Dynamical Systems vol. 28 , ( 4 ) 1081 - 1090 .
Morris ID ( 2008 ) . Maximizing measures of generic Hölder functions have zero entropy . Nonlinearity vol. 21 , ( 5 ) 993 - 1000 .
Morris ID ( 2007 ) . A sufficient condition for the subordination principle in ergodic optimization . Bulletin of the London Mathematical Society vol. 39 , ( 2 ) 214 - 220 .
Morris ID ( 2007 ) . Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type . Journal of Statistical Physics vol. 126 , ( 2 ) 315 - 324 .