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math.DS2025
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…
math.DS2025
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…