Bertrand-Mathis

· 1998

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math.DS · 2025-01-14 · accept · novelty 7.0

For non-integer β1, β2 > 1, the Rényi-Parry measures coincide if and only if β1 is a root of x^2 − qx − p = 0 with p ≤ q and β2 = β1 + 1.

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The coincidence of R\'{e}nyi-Parry measures for $\beta$-transformation math.DS · 2025-01-14 · accept · none · ref 1
For non-integer β1, β2 > 1, the Rényi-Parry measures coincide if and only if β1 is a root of x^2 − qx − p = 0 with p ≤ q and β2 = β1 + 1.