6 papers · 1 filter
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…
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…
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…
General real measurable Livšic regularity via transfer operators
Ian D. Morris
We prove a general measurable LivÅ¡ic regularity theorem for real-valued cocycles over non-invertible dynamical systems using only abstract hypotheses on an associated transfer ope…
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.…
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…