22 citations · 23 across the 5 of their papers we have counts for
8 papers · 1 filter
Prevalent uniqueness in ergodic optimisation
Ian D. Morris
One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space and for any Banach space of continuous real-valued functi…
A strongly irreducible affine iterated function system with two invariant measures of maximal dimension
Ian D. Morris, Cagri Sert
A classical theorem of Hutchinson asserts that if an iterated function system acts on by similitudes and satisfies the open set condition then it admits a unique sel…
Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone
Natalia Jurga, Ian Morris
The sub-additive pressure function for an affine iterated function system (IFS) and the affinity dimension, defined as the unique solution to , were introduc…
Effective estimates on the top Lyapunov exponent for random matrix products
Natalia Jurga, Ian Morris
We study the top Lyapunov exponents of random products of positive matrices and obtain an efficient algorithm for its computation. As in the earlier work of Pollicott,…
Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
Balázs Bárány, Antti Käenmäki, Ian D. Morris
In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful…
Some observations on Käenmäki measures
Ian D. Morris
In this note we investigate some properties of equilibrium states of affine iterated function systems, sometimes known as Käenmäki measures. We give a simple sufficient condition f…