![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
We completely determine the median of the entrance time function for the one-parameter standard family of flat spot maps. The function mapping parameters to medians is shown to be a countably piecewise affine degree-one homeomorphism, with uncountably many cusps and precisely nine critical points.
Notes
Notes
1. Throughout we shall use ∫ g to denote the Lebesgue integral of a function g on the whole circle 𝕋, and ∫
A
g or for its Lebesgue integral over the set A or interval [a, b].
2. The terminology Sturmian is due to Morse and Hedlund Citation15, who studied the 0–1 sequences corresponding to the binary expansions of points in Sturmian sets. These Sturmian sequences have since then been extensively investigated, see e.g. Citation5,Citation14,Citation16–19 for further characterizations and properties.
3. Uniqueness is because e γ is strictly positive on 𝕋 ∖ F γ = [γ, γ + 1/2].