Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in A_α(M) for arbitrary Liouvillean number α

2015/11/30 by Roland Gunesch, Gunesch, Roland, Philipp Kunde +1
Computer Science · Mathematics · #37A05 (Primary) #37C40 #53C99 (Secondary) #57R50 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1512.00075

openalex publication_date 2015/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We show that on any smooth compact connected manifold of dimension m≥ 2 admitting a smooth non-trivial circle action S = \S_t\_{t ∈ ℝ}, S_t+1=S_t, the set of weakly mixing C^∞-diffeomorphisms which preserve both a smooth volume ν and a measurable Riemannian metric is dense in A_α (M)= \h ∘ S_α ∘ h^-1 : h ∈ Diff^∞(M, ν) \^C^∞ for every Liouvillean number α. The proof is based on a quantitative version of the Anosov-Katok-method with explicitly constructed conjugation maps and partitions.

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