## Institute for Mathematical Sciences

## Preprint ims94-8

** A. Epstein, L. Keen, & C. Tresser**
* The Set of Maps F_{a,b}: x -> x+a+{b/{2 pi}} sin(2 pi x) with any Given Rotation Interval is Contractible.*

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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