# Bi-rational maps in four dimensions with two invariants

## TL;DR

This paper introduces a class of four-dimensional bi-rational maps with two invariants, analyzing their integrability through degree growth and Liouville theory, contributing to the understanding of complex dynamical systems.

## Contribution

It presents a new class of four-dimensional bi-rational maps with specific invariants and explores their integrability properties, advancing the study of higher-dimensional discrete integrable systems.

## Key findings

- Maps exhibit controlled degree growth indicating integrability
- Liouville integrability confirmed for the proposed maps
- Provides new examples of higher-dimensional integrable maps

## Abstract

In this paper we present a class of four-dimensional bi-rational maps with two invariants satisfying certain constraints on degrees. We discuss the integrability properties of these maps from the point of view of degree growth and Liouville integrability.