Spectral orthogonality of special flows

2025/11/25 by Sheng, Mingcheng
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.20825

Abstract

In this paper, we study the spectral orthogonality problem for special flows built over irrational rotations under two different types of roof functions: 1) the roof functions are real analytic. 2) the roof functions are piecewise C¹ with one discontinuity. These flows are also known as von-Neumann flows. We show that if \T^f_α\ is as in 1) and weak mixing, then for a G_δ dense set of β, we have that \T^f_β\ is weak-mixing and is spectrally orthogonal to \T^f_α\. On the other hand, if \T^f_α\ is as in 2), then for a full measure set of β, the flows \T^f_α\ and \T^f_β\ are spectrally orthogonal.

Citations

• Singularity of the spectrum of typical minimal smooth area-preserving flows in any genus
• On disjointness properties of some parabolic flows
• On isomorphism problem for von Neumann flows with one discontinuity

Related

• A Dichotomy between Discrete and Continuous Spectrum for a Class of Special Flows over Rotations
• Ratner's property and mixing for special flows over two-dimensional rotations
• Ratner's property for special flows over irrational rotations under\n functions of bounded variation. II
• Mild mixing property for special flows under piecewise constant functions
• On mild mixing of special flows over irrational rotations under piecewise smooth functions