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 by Adam Epstein, Epstein, Adam, Linda Keen +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/9405216

openalex publication_date 1994/05/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Consider the two-parameter family of real analytic maps F_a,b:x ↦ x+ a+b\over 2π sin(2πx) 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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