Horocyclic trajectories in hyperbolic solenoidal surfaces of finite type

TL;DR

This paper investigates the dynamical behavior of horocycle flows on hyperbolic solenoidal surfaces of finite type, extending classical surface dynamics to a lamination setting.

Contribution

It introduces the study of horocyclic trajectories on hyperbolic solenoidal surfaces, a novel extension of hyperbolic surface dynamics to lamination structures.

Findings

Analysis of horocycle flow properties on solenoidal surfaces

Identification of ergodic and mixing behaviors in the lamination context

Extension of classical hyperbolic surface results to solenoidal manifolds

Abstract

We study the dynamical properties of the laminated horocycle flow on the unit tangent bundles of 2-dimensional smooth solenoidal manifolds of finite type. These laminations are the analog of complete hyperbolic surfaces of finite area.