On the strong convolution singularity property

2012/11/16 by Joanna Kułaga-Przymus, Kułaga-Przymus, Joanna
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1211.4007

openalex publication_date 2012/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type has simple spectrum. We use these methods to give examples of smooth flows on closed orientable surfaces of genus at least 2 with a weaker property: each of their maximal spectral types σ is such that the Gaussian system induced by σ has simple spectrum on the so-called 3rd chaos (i.e. V_σ^{\odot 3} has simple spectrum).

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