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math.DS 1

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Concentration of dimension in the Lagrange spectrum

math.DS · 2024-11-25 · conditional · novelty 6.0

For conservative horseshoes and for the classical Lagrange spectrum, the equality HD(k^{-1}(t)) = HD(k^{-1}(-∞,t]) holds precisely for t in a strictly increasing 'J' set, up to a countable exceptional set.

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  • Concentration of dimension in the Lagrange spectrum math.DS · 2024-11-25 · conditional · none · ref 2

    For conservative horseshoes and for the classical Lagrange spectrum, the equality HD(k^{-1}(t)) = HD(k^{-1}(-∞,t]) holds precisely for t in a strictly increasing 'J' set, up to a countable exceptional set.