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Preprints, Working Papers, ... Year : 2018

Classification of generic semigroup actions of circle diffeomorphisms

Abstract

We study topological properties of semi-group actions on the circle by orientation-preserving homeomorhisms. We prove that a generic action either possesses a forward-invariant interval-domain (i.e. a finite union of disjoint circle arcs), or is two-sided minimal (and, moreover, by a small perturbation one can create a map with arbitrary rotation number in the semigroup). For the minimal case, we also study conditions required for global synchronization.

Dates and versions

hal-01762157 , version 1 (09-04-2018)

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Cite

Victor A. Kleptsyn, Yury Kudryashov, Alexey Okunev. Classification of generic semigroup actions of circle diffeomorphisms. 2018. ⟨hal-01762157⟩
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