61 citations · 117 across the 30 of their papers we have counts for
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math.DS2016
A necessary and sufficient condition for a matrix equilibrium state to be mixing
Ian D. Morris
Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to Hölder-continuous real-valued potentials. The construction of equilibrium states…
math.DS2016
Ergodic properties of matrix equilibrium states
Ian D. Morris
Given a finite irreducible set of real matrices and a real parameter , there exists a unique shift-invariant equilibrium state associated to $(A_…
math.DS2016
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
Ian D. Morris, Pablo Shmerkin
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-…