# On a two dimensional dynamical system generated by the floor function

## TL;DR

This paper studies a two-dimensional dynamical system created by the floor function, analyzing how its long-term behavior varies with different parameters and initial conditions.

## Contribution

It provides a comprehensive description of all limit points of the system depending on the parameter and initial point, advancing understanding of floor function-based dynamics.

## Key findings

- Characterization of limit points for various parameter values
- Dependence of system behavior on initial conditions
- Identification of stable and unstable regimes

## Abstract

In this paper we investigate the two dimensional dynamical system generated by the floor function with a parameter $\lambda\in \R$. We describe all limit points of the dynamical system depending on $\lambda$ and on the initial point.