The Romik map yields a strange continued fraction with partial quotients restricted to {0, ±2}, an ergodic natural extension with explicit sigma-finite measure, and the property that asymptotically half of regular continued fraction convergents coincide with Romik convergents for Lebesgue-almost-1 x
Kraaikamp – Metrical theory of continued fractions
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A strange continued fraction associated with the Romik map
The Romik map yields a strange continued fraction with partial quotients restricted to {0, ±2}, an ergodic natural extension with explicit sigma-finite measure, and the property that asymptotically half of regular continued fraction convergents coincide with Romik convergents for Lebesgue-almost-1 x