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

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

1994-05-14

arxiv.org/abs/math/9405216v1

Mathematics

Dynamical Systems

Scientific paper

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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