48 citations · 69 across the 9 of their papers we have counts for
10 papers
A Poincaré-Bendixson theorem for Bebutov shifts and applications to switched systems
Jairo Bochi, Ian D. Morris
We prove a version of the Poincaré-Bendixson theorem for certain classes of curves on the 2-sphere which are not required to be the trajectories of an underlying flow or semiflow o…
Stability with respect to periodic switching laws does not imply global stability under arbitrary switching
Ian D. Morris
R. Shorten, F. Wirth, O. Mason, K. Wulff and C. King have asked whether a linear switched system is guaranteed to be globally uniformly stable under arbitrary switching if it is kn…
Continuity and approximability of competitive spectral radii
Marianne Akian, Stéphane Gaubert, Loïc Marchesini +1
The competitive spectral radius extends the notion of joint spectral radius to the two-player case: two players alternatively select matrices in prescribed compact sets, resulting…
General real measurable Livšic regularity via transfer operators
Ian D. Morris
We prove a general measurable Livšic regularity theorem for real-valued cocycles over non-invertible dynamical systems using only abstract hypotheses on an associated transfer oper…
Projections of self-affine fractals
Ian Morris, Cagri Sert
We extend Falconer's 1988 landmark result on the dimensions of self-affine fractals to encompass the dimensions of their projections, showing furthermore that their families of exc…
Thermodynamic formalism of countably generated self-affine sets
Antti Käenmäki, Ian D. Morris
In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earli…
Exceptional projections of self-affine sets: an introduction
Ian D. Morris
We describe some recent results on the dimensions of linear projections of self-affine fractals, focusing in particular on an upper bound for the dimension of the projected image.…
Path-dependent shrinking targets in generic affine iterated function systems
Henna Koivusalo, Lingmin Liao, Ian Morris +1
We calculate the Hausdorff dimension of shrinking target sets of symbolic balls in generic affine iterated function systems with matrix norms bounded by . Relative to ea…
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
Antti Käenmäki, Ian D. Morris
A fundamental problem in the dimension theory of self-affine sets is the construction of high-dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the…
Continuity properties of the lower spectral radius
Jairo Bochi, Ian D. Morris
The lower spectral radius, or joint spectral subradius, of a set of real matrices is defined to be the smallest possible exponential growth rate of long products of ma…