Dr Ian Morris


Qualifications: MMath Mathematics (Warwick 2001), PhD Mathematics (Manchester 2006)

Phone: Work: 01483 68 6510
Room no: 29 AA 04

Further information

Research Interests

My area of research interest is ergodic theory. As well as using ergodic theory to study dynamical systems, I am interested in applications of ergodic theory to other areas of mathematics including the analysis of algorithms, Ramsey theory, and matrix analysis. I have recently been particularly involved in the use of ergodic theory to study joint spectral characteristics of sets of linear operators.


The following list of published and accepted articles is complete as of October 2013:

  • Extremal sequences of polynomial complexity, Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013) 191–205.
  • On a Devil's staircase associated to the joint spectral radii of a family of pairs of matrices (with Nikita Sidorov), Journal of the European Mathematical Society 15 (2013) 1747–1782.
  • Mather sets for sequences of matrices and applications to the study of joint spectral radii, Proceedings of the London Mathematical Society 107 (2013) 121–150.
  • A new sufficient condition for the uniqueness of Barabanov norms, SIAM Journal of Matrix Analysis and Applications 33 (2012) 317–324.
  • The generalised Berger-Wang formula and the spectral radius of linear cocycles,  Journal of Functional Analysis 262 (2012) 811–824.
  • An explicit counterexample to the Lagarias-Wang finiteness conjecture (with Kevin G. Hare, Nikita Sidorov and Jacques Theys),  Advances in Mathematics 226 (2011) 4667–4701.
  • A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory,  Advances in Mathematics 225 (2010) 3425–3445.
  • Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms, Linear Algebra and its Applications 443 (2010) 1301–1311.
  • Ergodic optimisation for generic continuous functions, Discrete and Continuous Dynamical Systems: Series A 27 (2010) 383–388.
  • The Conze-Guivarc'h-Mañé lemma for intermittent maps of the circle, Ergodic Theory and Dynamical Systems 29 (2009) 1603–1611.
  • Lyapunov optimizing measures for C¹ expanding maps of the circle (with Oliver Jenkinson), Ergodic Theory and Dynamical Systems 28 (2008) 1849–1860.
  • Approximating the maximum ergodic average via periodic orbits (with David Collier), Ergodic Theory and Dynamical Systems 28 (2008) 1081–1090.
  • Maximising measures of generic Hölder continuous potentials have zero entropy,  Nonlinearity 21 (2008) 993–1000.
  • A sufficient condition for the subordination principle in ergodic optimisation, Bulletin of the London Mathematical Society 39 (2007) 214–220.
  • Entropy for zero-temperature limits of Gibbs-equilibrium states for countable-alphabet subshifts of finite type,  Journal of Statistical Physics 126 (2007) 315–324.

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