# Rational map ax+1/x on the projective line over $\mathbb{Q}_2$

## TL;DR

This paper fully characterizes the dynamical behavior of the rational map ax+1/x on the projective line over the 2-adic numbers, revealing detailed structure specific to the field Q2.

## Contribution

It provides a complete description of the dynamical structure of the map on the projective line over Q2, a novel analysis in 2-adic dynamics.

## Key findings

- Complete dynamical classification over Q2
- Identification of fixed points and cycles
- Description of invariant sets and measures

## Abstract

The dynamical structure of the rational map $ax+1/x$ on the projective line over the field Q2 of $2$-adic numbers, is fully described.