# Dynamics of induced homeomorphisms of one-dimensional solenoids

## TL;DR

This paper investigates the behavior of homeomorphisms on one-dimensional solenoids, characterizing their lifting properties and dynamics through rotation theory, enhancing understanding of their topological and dynamical structure.

## Contribution

It provides a new characterization of the lifting property for a dense subgroup of the isotopy component and describes the dynamics using rotation theory.

## Key findings

- Characterization of the lifting property for an open dense subgroup
- Description of dynamics via rotation theory
- Insights into the structure of homeomorphisms on solenoids

## Abstract

We study the displacement function of homeomorphisms isotopic to the identity of the universal one-dimensional solenoid and we get a characterization of the lifting property for an open and dense subgroup of the isotopy component of the identity. The dynamics of an element in this subgroup is also described using rotation theory.