Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
Random walks on finite volume homogeneous spaces
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Almost every point on affine subspaces in horospheres is Birkhoff generic except in cases of high Diophantine exponent or approximability by number-field subspaces.
An effective multi-equidistribution result for diagonal translates of unipotent flows is established, yielding a central limit theorem in inhomogeneous Diophantine approximation for non-Liouville shifts.
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Uniformly Positive Mean Dimension
Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
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Birkhoff genericity on affine subspaces in horospheres
Almost every point on affine subspaces in horospheres is Birkhoff generic except in cases of high Diophantine exponent or approximability by number-field subspaces.