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math.DS 1

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2026 1

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Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action

math.DS · 2026-05-20 · unverdicted · novelty 6.0

For systems satisfying approximate Z^d or Z_+^d-product property and asymptotic entropy expansiveness, ergodic measures with any given intermediate entropy are generic in certain natural subspaces, confirming Katok's conjecture.

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  • Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action math.DS · 2026-05-20 · unverdicted · none · ref 1

    For systems satisfying approximate Z^d or Z_+^d-product property and asymptotic entropy expansiveness, ergodic measures with any given intermediate entropy are generic in certain natural subspaces, confirming Katok's conjecture.