The structure of periodic point free distal homeomorphisms on the annulus

2024/06/15 by Shi, Enhui, Xu, Hui, YU, Ziqi
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.10674

Abstract

Let A be an annulus in the plane \mathbb R² and g:A→ A be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is a continuous decomposition of A into g-invariant circles such that all the restrictions of g on them share a common irrational rotation number and all these circles are linearly ordered by the inclusion relation on the sets of bounded components of their complements in \mathbb R².

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