2023/05/30 by Bo Han, Han, Bo, Xiao Wen +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2305.18692
openalex publication_date 2023/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the centralizer of a separating continuous flow without fixed points. We show that if M is a compact metric space and ϕt:M→ M is a separating flow without fixed points, then ϕt has a quasi-trivial centralizer, that is, if a continuous flow ψt commutes with ϕt, then there exists a continuous function A: M→ℝ which is invariant along the orbit of ϕt such that ψt(x)=ϕA(x)t(x) holds for all x∈ M. We also show that if M is a compact Riemannian manifold without boundary and Φu is a separating C1 ℝd-action on M, then Φu has a quasi-trivial centralizer, that is, if Ψu is a ℝd-action on M commuting with Φu, then there is a continuous map A: M\toMd× d(ℝ) which is invariant along orbit of Φu such that Ψu(x)=ΦA(x)u(x) for all x∈ M. These improve Theorem 1 of \citeO and Theorem 2 of \citeBRV respectively.