A dynamical construction of Liouville domains

TL;DR

This paper introduces a new method for constructing Liouville domains using partial mapping tori and explores examples involving hyperbolic dynamics such as Smale's attractor and hyperbolic toral automorphisms.

Contribution

It provides a novel dynamical construction of Liouville domains and analyzes their properties through examples with hyperbolic monodromies.

Findings

Construction of Liouville domains via partial mapping tori

Analysis of hyperbolic monodromies in specific examples

Insights into dynamical systems within symplectic geometry

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.