2012/06/26 by V. V. Ryzhikov, Ryzhikov, V. V.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1206.6093
Ergodic Theory. Lecture notes
openalex publication_date 2012/06/26 · arxiv created 2012/06/27 · arxiv updated 2012/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In connection with Rokhlin's question on an automorphism with a homogeneous nonsimple spectrum, we indicate a class of measure-preserving maps T such that T× T has a homogeneous spectrum of multiplicity 2. The automorphisms in question satisfy the condition σ∗σ⊥ σ, where σ is the spectral measure of T. We also show that there is a mixing automorphism possessing the above properties and their higher order analogs. This work has been published in the pilot issue of Selected Russian Mathematics, Vol.1 (1999), no.1, 13-24.