2019/12/10 by В. С. Медведев, Medvedev, V., Евгений Викторович Жужома +1
Mathematics · Physics and Astronomy · #34C40 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37D05 #Quantum chaos and dynamical systems #Secondary 37B35
paper · pdf · doi:10.48550/arxiv.1912.04499
openalex publication_date 2019/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that given any closed n-manifold Mn, n≥ 4, there is an A-flow ft on Mn such that the non-wandering set NW(ft) consists of 2-dimensional expanding attractor (the both, orientable and non-orientable) and trivial basic sets. For 3-manifolds, we prove that given any closed 3-manifold M3, there is an A-flow ft on M3 such that the non-wandering set NW(ft) consists of a non-orientable 2-dimensional expanding attractor and trivial basic sets. Moreover, there is a nonsingular A-flow ft on a 3-sphere such that the non-wandering set NW(ft) consists of an orientable 2-dimensional expanding attractor and trivial basic sets (isolated periodic trajectories).