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.
Entropyandthelocalization ofeigenfunctions
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A singular delta potential supported on an equator of S^2 permits sequences of eigenfunctions whose semiclassical measures are not invariant under geodesic flow, with asymptotic concentration on one hemisphere.
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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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Quantum Limits of the Laplacian perturbed along a geodesic on $\mathbb{S}^{2}$
A singular delta potential supported on an equator of S^2 permits sequences of eigenfunctions whose semiclassical measures are not invariant under geodesic flow, with asymptotic concentration on one hemisphere.