Abstract
We classify the dynamics of (orientation-preserving) flat spot maps on the circle, and derive explicit expressions for the function counting the first entrance time into the flat spot. Metric properties of first entrance time functions for the standard flat spot family are analysed in detail, via a computation of conditional expectation with respect to the orbit partition. This facilitates investigation of the median of the entrance time function, proving the surprising result that its first entrance time is constrained to equal either 1, 2, 4, 5 or 12, provided the rotation number of the flat spot map does not equal the exceptional values 0, ±2/7, ±3/10, ±1/3, ±3/8.
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