On Mixing Flows on Finite Area Translation Surfaces

2025/08/26 by Gordillo, Erick
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.19139

Abstract

We construct an explicit family of finite-area, infinite-genus translation surfaces whose vertical translation flow is strongly mixing. This provides a positive answer to a question posed by Lindsey and Treviño~\citeLT

Citations

• Infinite Translation Surfaces in the Wild
• Mixing of asymmetric logarithmic suspension flows over interval exchange transformations
• Weak mixing for interval exchange transformations and translation flows
• Mixing on a class of rank one transformations

Related

• A smooth mixing flow on a surface with non-degenerate fixed points
• Weak mixing for interval exchange transformations and translation flows
• Multiple mixing and parabolic divergence in smooth area-preserving flows\n on higher genus surfaces
• Infinite Translation Surfaces in the Wild
• Absence of mixing in area-preserving flows on surfaces