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math.DS2025
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…
math.DS2025
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…
math.DS2025
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…