4 papers
Cut and project schemes in the Poincaré disc: From cocompact Fuchsian groups to chaotic Delone sets
Richard A. Howat, Tony Samuel, AyÅe Yıltekin-KarataÅ
A question raised by Davies et al [Phys. Rev. Lett. 131, 2023] is: "Can developing new cut and project models, where the lattice is not square or the curve is non-linear, generate…
Rauzy fractals of random substitutions
Philipp Gohlke, Andrew Mitchell, Dan Rust +1
We develop a theory of Rauzy fractals for random substitutions, which are a generalisation of deterministic substitutions where the substituted image of a letter is determined by a…
The matrix potential game and structures of self-affine sets
Richard A. Howat, Andrew Mitchell, Tony Samuel
We present a new variant of the potential game and show that certain compact subsets of , including a large class of self-affine sets, are winning in our game. We pro…
The shadowing property for piecewise monotone interval maps
Adarsh Bura, Chris Good, Tony Samuel
The property of shadowing has been shown to be fundamental in both the theory of symbolic dynamics as well as continuous dynamical systems. A quintessential class of discontinuous…