A dynamical construction of Liouville domains

2019/10/30 by Yang Huang, Huang, Yang
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1910.14132

openalex publication_date 2019/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first present a general construction of Liouville domains as partial mapping tori. Then we study two examples where the (partial) monodromies exhibit certain hyperbolic behavior in the sense of Dynamical Systems. The first example is based on Smale's attractor, a.k.a., solenoid; and the second example is based on certain hyperbolic toral automorphisms.

Citations

• Symplectic manifolds with contact type boundaries
• Convex hypersurface theory in contact topology

Related

• Zeta functions of dynamically tame Liouville domains
• Torus bundle Liouville domains are stably Weinstein
• Ideal Liouville Domains - a cool gadget
• Dynamical models for Liouville and obstructions to further progress on sign patterns
• Partial hyperbolicity and attracting regions in 3-dimensional manifolds