Greedy and lazy maps for double base expansions each admit a unique ACIM equivalent to Lebesgue on given intervals, are exact, and almost every point has continuum many expansions under q0+q1 > q0 q1.
Sidorov, Expansions in non-integer bases: lower, middle and top orders.J
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Invariant measure for double base expansions
Greedy and lazy maps for double base expansions each admit a unique ACIM equivalent to Lebesgue on given intervals, are exact, and almost every point has continuum many expansions under q0+q1 > q0 q1.