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The set of maps F_{a,b}: x -> x+a+{b/{2 pi}} sin(2 pi x) with any given rotation interval is contractible

Adam Epstein·Linda Keen·Charles Tresser
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Abstract

Consider the two-parameter family of real analytic maps $F_{a,b}:x \mapsto x+ a+{b\over 2\pi} \sin(2\pi x)$ which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed interval $I$, the set of maps $F_{a,b}$ whose rotation interval is $I$, form a contractible set.

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Adam Epstein, Linda Keen, Charles Tresser. 1994-05-14. The set of maps F_{a,b}: x -> x+a+{b/{2 pi}} sin(2 pi x) with any given rotation interval is contractible. https://arxiv.org/abs/math/9405216

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